Chapter Manual Calculations 2-1 2-2 2-3 2-4 2-5 2-6 2-7 2-8 Basic Calculations Special Functions Specifying the Angle Unit and Display Format Function Calculations Numerical Calculations Complex Number Calculations Binary, Octal, Decimal, and Hexadecimal Calculations Matrix Calculations 20010101 2
-1-1 Basic Calculations 2-1 Basic Calculations k Arithmetic Calculations • Enter arithmetic calculations as they are written, from left to right. • Use the - key to input the minus sign before a negative value. • Calculations are performed internally with a 15-digit mantissa. The result is rounded to a 10-digit mantissa before it is displayed. • For mixed arithmetic calculations, multiplication and division are given priority over addition and subtraction. Example Operation 23 + 4.5 – 53 = –25.5 23+4.
2-1-2 Basic Calculations k Number of Decimal Places, Number of Significant Digits, Normal Display Range [SET UP]- [Display] -[Fix] / [Sci] / [Norm] • Even after you specify the number of decimal places or the number of significant digits, internal calculations are still performed using a 15-digit mantissa, and displayed values are stored with a 10-digit mantissa.
2-1-3 Basic Calculations ○ ○ ○ ○ ○ Example 200 ÷ 7 × 14 = 400 Condition 3 decimal places Operation Display 200/7*14w u3(SET UP)cccccccccc 1(Fix)dwiw Calculation continues using display capacity of 10 digits 200/7w * 14w 400 400.000 28.571 Ans × 400.000 • If the same calculation is performed using the specified number of digits: 200/7w The value stored internally is rounded off to the number of decimal places you specify. K5(NUM)e(Rnd)w * 14w 28.571 28.571 Ans × 399.
2-1-4 Basic Calculations 3 Power/root ^(xy), x 4 Fractions a b/c 5 Abbreviated multiplication format in front of π, memory name, or variable name. 2π, 5A, Xmin, F Start, etc. 6 Type B functions With these functions, the function key is pressed and then the value is entered.
2-1-5 Basic Calculations k Multiplication Operations without a Multiplication Sign You can omit the multiplication sign (×) in any of the following operations. • Before coordinate transformation and Type B functions (1 on page 2-1-3 and 6 on page 2-1-4), except for negative signs ○ ○ ○ ○ ○ Example 2sin30, 10log1.2, 2 , 2Pol(5, 12), etc. • Before constants, variable names, memory names ○ ○ ○ ○ ○ Example 2π, 2AB, 3Ans, 3Y1 , etc. • Before an open parenthesis ○ ○ ○ ○ ○ Example 3(5 + 6), (A + 1)(B – 1), etc.
2-1-6 Basic Calculations • When you try to perform a calculation that causes memory capacity to be exceeded (Memory ERROR). • When you use a command that requires an argument, without providing a valid argument (Argument ERROR). • When an attempt is made to use an illegal dimension during matrix calculations (Dimension ERROR). • When you are in the real mode and an attempt is made to perform a calculation that produces a complex number solution.
2-2-1 Special Functions 2-2 Special Functions k Calculations Using Variables Example Operation Display 193.2aav(A)w 193.2 193.2 ÷ 23 = 8.4 av(A)/23w 8.4 193.2 ÷ 28 = 6.9 av(A)/28w 6.9 k Memory u Variables This calculator comes with 28 variables as standard. You can use variables to store values you want to use inside of calculations. Variables are identified by single-letter names, which are made up of the 26 letters of the alphabet, plus r and θ .
2-2-2 Special Functions u To display the contents of a variable ○ ○ ○ ○ ○ Example To display the contents of variable A Aav(A)w u To clear a variable ○ ○ ○ ○ ○ Example To clear variable A Aaaav(A)w u To assign the same value to more than one variable [value]a [first variable name*1]K6(g)6(g)4(SYBL)d(~) [last variable name*1]w ○ ○ ○ ○ ○ Example To assign a value of 10 to variables A through F Abaaav(A) K6(g)6(g)4(SYBL)d(~) at(F)w u Function Memory [OPTN]-[FMEM] Function memory (f 1~f20) is conveni
2-2-3 Special Functions u To store a function ○ ○ ○ ○ ○ Example To store the function (A+B) (A–B) as function memory number 1 (av(A)+al(B)) (av(A)-al(B)) K6(g)5(FMEM) b(Store)bw u To recall a function ○ ○ ○ ○ ○ Example To recall the contents of function memory number 1 K6(g)5(FMEM) c(Recall)bw u To display a list of available functions K6(g)5(FMEM) e(SEE) # If the function memory number to which you store a function already contains a function, the previous function is replaced with the new one.
2-2-4 Special Functions u To delete a function ○ ○ ○ ○ ○ Example To delete the contents of function memory number 1 AK6(g)5(FMEM) b(Store)bw • Executing the store operation while the display is blank deletes the function in the function memory you specify. u To use stored functions ○ ○ ○ ○ ○ Example To store x3 + 1, x2 + x into function memory, and then graph: y = x3 + x2 + x + 1 Use the following View Window settings.
2-2-5 Special Functions k Answer Function The Answer Function automatically stores the last result you calculated by pressing w(unless the w key operation results in an error). The result is stored in the answer memory. u To use the contents of the answer memory in a calculation ○ ○ ○ ○ ○ Example 123 + 456 = 579 789 – 579 = 210 Abcd+efgw hij-!-(Ans)w k Performing Continuous Calculations Answer memory also lets you use the result of one calculation as one of the arguments in the next calculation.
2-2-6 Special Functions k Stacks The unit employs memory blocks, called stacks, for storage of low priority values and commands. There is a 10-level numeric value stack, a 26-level command stack, and a 10level program subroutine stack. An error occurs if you perform a calculation so complex that it exceeds the capacity of available numeric value stack or command stack space, or if execution of a program subroutine exceeds the capacity of the subroutine stack.
2-2-7 Special Functions k Using Multistatements Multistatements are formed by connecting a number of individual statements for sequential execution. You can use multistatements in manual calculations and in programmed calculations. There are two different ways that you can use to connect statements to form multistatements. • Colon (:) Statements that are connected with colons are executed from left to right, without stopping.
2-3-1 Specifying the Angle Unit and Display Format 2-3 Specifying the Angle Unit and Display Format Before performing a calculation for the first time, you should use the SET UP screen to specify the angle unit and display format. k Setting the Angle Unit [SET UP]- [Angle] 1. On the Set Up screen, highlight “Angle”. 2. Press the function key for the angle unit you want to specify, then press i. • {Deg}/{Rad}/{Gra} ...
2-3-2 Specifying the Angle Unit and Display Format u To specify the number of significant digits (Sci) ○ ○ ○ ○ ○ Example To specify three significant digits 2(Sci) dw Press the function key that corresponds to the number of significant digits you want to specify (n = 0 to 9). u To specify the normal display (Norm 1/Norm 2) Press 3(Norm) to switch between Norm 1 and Norm 2. Norm 1: 10–2 (0.01)>|x|, |x| >1010 Norm 2: 10–9 (0.
2-4-1 Function Calculations 2-4 Function Calculations k Function Menus This calculator includes five function menus that give you access to scientific functions not printed on the key panel. • The contents of the function menu differ according to the mode you entered from the Main Menu before you pressed the K key. The following examples show function menus that appear in the RUN • MAT Mode. u Numeric Calculations (NUM) [OPTN]-[NUM] • {Abs} ...
2-4-2 Function Calculations u Hyperbolic Calculations (HYP) [OPTN]-[HYP] • {sinh}/{cosh}/{tanh} ... hyperbolic {sine}/{cosine}/{tangent} • {sinh–1 }/{cosh–1}/{tanh–1 } ... inverse hyperbolic {sine}/{cosine}/{tangent} u Angle Units, Coordinate Conversion, Sexagesimal Operations (ANGL) [OPTN]-[ANGL] • {°}/{r}/{g} ... {degrees}/{radians}/{grads} for a specific input value • {° ’ ”} ... {specifies degrees (hours), minutes, seconds when inputting a degrees/minutes/ seconds value} • {' DMS} ...
2-4-3 Function Calculations k Trigonometric and Inverse Trigonometric Functions • Be sure to set the angle unit before performing trigonometric function and inverse trigonometric function calculations. π (90° = ––– radians = 100 grads) 2 • Be sure to specify Comp for Mode in the SET UP screen. Example sin 63° = 0.8910065242 π rad) = 0.5 cos (–– 3 Operation u3(SET UP)cccc1(Deg)i s63w u3(SET UP)cccc2(Rad)i c(!E(π)/d)w tan (– 35gra) = – 0.6128007881 u3(SET UP)cccc3(Gra)i t-35w 2 • sin 45° × cos 65° = 0.
2-4-4 Function Calculations k Logarithmic and Exponential Functions • Be sure to specify Comp for Mode in the SET UP screen. Example Operation log 1.23 (log10 1.23) = 8.990511144 × 10–2 l1.23w In 90 (loge90) = 4.49980967 I90w 101.23 = 16.98243652 (To obtain the antilogarithm of common logarithm 1.23) !l(10x)1.23w e4.5 = 90.0171313 (To obtain the antilogarithm of natural logarithm 4.5) !I(ex)4.
2-4-5 Function Calculations k Hyperbolic and Inverse Hyperbolic Functions • Be sure to specify Comp for Mode in the SET UP screen. Example Operation sinh 3.6 = 18.28545536 K6(g)2(HYP)b(sinh)3.6w cosh 1.5 – sinh 1.5 = 0.2231301601 = e –1.5 (Display: –1.5) K6(g)2(HYP)c(cosh)1.52(HYP)b(sinh)1.5w I!-(Ans)w (Proof of cosh x ± sinh x = e ±x) cosh–1 20 15 = 0.7953654612 K6(g)2(HYP)f(cosh–1 )(20/15)w Determine the value of x when tanh 4 x = 0.88 –1 x = tanh 0.88 K6(g)2(HYP)g(tanh–1 )0.88/4w 4 = 0.
2-4-6 Function Calculations k Other Functions • Be sure to specify Comp for Mode in the SET UP screen. Example Operation 2 + 5 = 3.65028154 !x( )2+!x( (3 + i) = 1.755317302 +0.2848487846i !x( )(d+!a(i))w (–3) 2 = (–3) × (–3) = 9 (-3)xw –32 = –(3 × 3) = –9 -3xw 1 –––––– = 12 1 1 –– – –– 3 4 8! (= 1 × 2 × 3 × .... × 8) = 40320 3 36 × 42 × 49 = 42 What is the absolute value of 3 the common logarithm of ? 4 | log 34 | = 0.
2-4-7 Function Calculations k Random Number Generation (Ran#) This function generates a 10-digit truly random or sequentially random number that is greater than zero and less than 1. • A truly random number is generated if you do not specify anything for the argument. Example Operation Ran # (Generates a random number.) K6(g)1(PROB)e(Ran#)w (Each press of w generates a new random number.) w w • Specifying an argument from 1 to 9 generates random numbers based on that sequence.
2-4-8 Function Calculations k Coordinate Conversion u Rectangular Coordinates u Polar Coordinates • With polar coordinates, θ can be calculated and displayed within a range of –180°< θ < 180° (radians and grads have same range). • Be sure to specify Comp for Mode in the SET UP screen. Example Operation Calculate r and θ ° when x = 14 and y = 20.7 1 24.989 → 24.98979792 (r) 2 55.928 → 55.92839019 (θ) u3(SET UP)cccc1(Deg)i K6(g)3(ANGL)g(Pol() 14,20.7)w Calculate x and y when r = 25 and θ = 56° 1 13.
2-4-9 Function Calculations k Permutation and Combination u Permutation u Combination n! nPr = ––––– (n – r)! n! nCr = ––––––– r! (n – r)! • Be sure to specify Comp for Mode in the SET UP screen.
2-4-10 Function Calculations k Fractions • Fractional values are displayed with the integer first, followed by the numerator and then the denominator. • Be sure to specify Comp for Mode in the SET UP screen. Example Operation 2 1 13 –– + 3 –– = 3 ––– (Display: 3{13{20) 5 4 20 = 3.65 1 1 ––––– + ––––– = 6.066202547 × 10–4 2578 4572 2$5+3$1$4w $ (Conversion to decimal) $ (Conversion to fraction) 1$2578+1$4572w (Display: 6.066202547E –04*1 ) (Norm 1 display format) 1 –– × 0.5 = 0.25* 2 2 1 = –– 4 1$2*.
2-4-11 Function Calculations k Engineering Notation Calculations Input engineering symbols using the engineering notation menu. • Be sure to specify Comp for Mode in the SET UP screen. Example Operation 999k (kilo) + 25k (kilo) = 1.024M (mega) u3(SET UP)cccccccccc 4(Eng)i 999K5(NUM)g(E-SYM)g(k)+255(NUM) g(E-SYM)g(k)w 9 ÷ 10 = 0.9 = 900m (milli) = 0.9 = 0.0009k (kilo) = 0.
2-5-1 Numerical Calculations 2-5 Numerical Calculations The following describes the items that are available in the menus you use when performing differential/ quadratic differential, integration, Σ, maximum/minimum value, and Solve calculations. When the option menu is on the display, press 4(CALC) to display the function analysis menu. The items of this menu are used when performing specific types of calculations. • {d/dx}/{d2/dx2 }/{∫dx}/{Σ}/{FMin}/{FMax}/{Solve} ...
2-5-2 Numerical Calculations k Differential Calculations [OPTN]-[CALC]-[d /dx] To perform differential calculations, first display the function analysis menu, and then input the values shown in the formula below.
2-5-3 Numerical Calculations ○ ○ ○ ○ ○ Example To determine the derivative at point x = 3 for the function y = x3 + 4 x2 + x – 6, with a tolerance of “tol” = 1E – 5 Input the function f(x). AK4(CALC)b(d/dx)vMd+evx+v-g, Input point x = a for which you want to determine the derivative. d, Input the tolerance value. bE-f) w # In the function f(x), only X can be used as a variable in expressions.
2-5-4 Numerical Calculations u Applications of Differential Calculations • Differentials can be added, subtracted, multiplied or divided with each other. d d ––– f (a) = f '(a), ––– g (a) = g'(a) dx dx Therefore: f '(a) + g'(a), f '(a) × g'(a), etc. • Differential results can be used in addition, subtraction, multiplication, and division, and in functions. 2 × f '(a), log ( f '(a)), etc. • Functions can be used in any of the terms ( f (x), a, tol) of a differential. d ––– (sinx + cos x, sin0.
2-5-5 Numerical Calculations k Quadratic Differential Calculations [OPTN]-[CALC]-[d2 /dx2] After displaying the function analysis menu, you can input quadratic differentials using either of the two following formats.
2-5-6 Numerical Calculations u Quadratic Differential Applications • Arithmetic operations can be performed using two quadratic differentials. d2 d2 –––2 f (a) = f ''(a), –––2 g (a) = g''(a) dx dx Therefore: f ''(a) + g''(a), f ''(a) × g''(a), etc. • The result of a quadratic differential calculation can be used in a subsequent arithmetic or function calculation. 2 × f ''(a), log ( f ''(a) ), etc. • Functions can be used within the terms ( f(x), a, tol ) of a quadratic differential expression.
2-5-7 Numerical Calculations k Integration Calculations [OPTN]-[CALC]-[∫ dx] To perform integration calculations, first display the function analysis menu and then input the values in the formula shown below.
2-5-8 Numerical Calculations ○ ○ ○ ○ ○ Example To perform the integration calculation for the function shown below, with a tolerance of “tol” = 1 E - 4 ∫ 5 1 (2x2 + 3x + 4) dx Input the function f (x). AK4(CALC)d(∫dx)cvx+dv+e, Input the start point and end point. b,f, Input the tolerance value. bE-e) w u Application of Integration Calculation • Integrals can be used in addition, subtraction, multiplication or division. ∫ b a f(x) dx + ∫ d c g(x) dx, etc.
2-5-9 Numerical Calculations Note the following points to ensure correct integration values. (1) When cyclical functions for integration values become positive or negative for different divisions, perform the calculation for single cycles, or divide between negative and positive, and then add the results together.
2-5-10 Numerical Calculations k Σ Calculations [OPTN]-[CALC]-[Σ ] To perform Σ calculations, first display the function analysis menu, and then input the values shown in the formula below. K4(CALC)e(Σ) a k , k , α , β , n ) β Σ (a , k, α, β, n) = Σ a = a k α k k=α ○ ○ ○ ○ ○ Example + aα +1 +........+ aβ (n: distance between partitions) To calculate the following: 6 Σ (k 2 – 3k + 5) k=2 Use n = 1 as the distance between partitions.
2-5-11 Numerical Calculations u Σ Calculation Applications • Arithmetic operations using Σ calculation expressions n n k=1 k=1 Sn = Σ ak, Tn = Σ bk Expressions: Sn + Tn, Sn – Tn, etc. Possible operations: • Arithmetic and function operations using Σ calculation results 2 × Sn , log (Sn), etc. • Function operations using Σ calculation terms (ak , k) Σ (sink, k, 1, 5), etc.
2-5-12 Numerical Calculations k Maximum/Minimum Value Calculations [OPTN]-[CALC]-[FMin]/[FMax] After displaying the function analysis menu, you can input maximum/minimum calculations using the formats below, and solve for the maximum and minimum of a function within interval a < x < b.
2-5-13 Numerical Calculations ○ ○ ○ ○ ○ Example 2 To determine the maximum value for the interval defined by start point a = 0 and end point b = 3, with a precision of n = 6 for the function y = –x2 + 2 x + 2 Input f(x). AK4(CALC)g(FMax) -vx+cv+c, Input the interval a = 0, b = 3. a,d, Input the precision n = 6. g) w # In the function f(x ), only X can be used as a variable in expressions.
2-6-1 Complex Number Calculations 2-6 Complex Number Calculations You can perform addition, subtraction, multiplication, division, parentheses calculations, function calculations, and memory calculations with complex numbers just as you do with the manual calculations described on pages 2-1-1 and 2-4-6. You can select the complex number calculation mode by changing the Complex Mode item on the SET UP screen to one of the following settings. • {Real} ...
2-6-2 Complex Number Calculations k Absolute Value and Argument [OPTN]-[CPLX]-[Abs]/[Arg] The unit regards a complex number in the form a + bi as a coordinate on a Gaussian plane, and calculates absolute value Z and argument (arg).
2-6-3 Complex Number Calculations k Conjugate Complex Numbers [OPTN]-[CPLX]-[Conjg] A complex number of the form a + bi becomes a conjugate complex number of the form a – bi. ○ ○ ○ ○ ○ Example To calculate the conjugate complex number for the complex number 2 + 4i AK3(CPLX)d(Conjg) (c+e!a(i))w k Extraction of Real and Imaginary Parts [OPTN]-[CPLX]-[ReP]/[lmP] Use the following procedure to extract the real part a and the imaginary part b from a complex number of the form a + bi.
2-6-4 Complex Number Calculations k Polar Form and Rectangular Transformation [OPTN]-[CPLX]-[' re ^ θ i] Use the following procedure to transform a complex number displayed in rectangular form to polar form, and vice versa.
2-7-1 Binary, Octal, Decimal, and Hexadecimal Calculations with Integers 2-7 Binary, Octal, Decimal, and Hexadecimal Calculations with Integers You can use the RUN • MAT Mode and binary, octal, decimal, and hexadecimal settings to perform calculations that involve binary, octal, decimal and hexadecimal values. You can also convert between number systems and perform bitwise operations. • You cannot use scientific functions in binary, octal, decimal, and hexadecimal calculations.
2-7-2 Binary, Octal, Decimal, and Hexadecimal Calculations with Integers • The following are the calculation ranges for each of the number systems.
2-7-3 Binary, Octal, Decimal, and Hexadecimal Calculations with Integers k Selecting a Number System You can specify decimal, hexadecimal, binary, or octal as the default number system using the set up screen. After you press the function key that corresponds to the system you want to use, press w. u To specify a number system for an input value You can specify a number system for each individual value you input. Press 1(d~o) to display a menu of number system symbols.
2-7-4 Binary, Octal, Decimal, and Hexadecimal Calculations with Integers ○ ○ ○ ○ ○ Example 2 To input and execute 1238 × ABC 16, when the default number system is decimal or hexadecimal u3(SET UP)2(Dec)i A1(d~o)e(o)bcd* 1(d~o)c(h)ABC*1w 3(DISP)c(Hex)w k Negative Values and Bitwise Operations Press 2(LOGIC) to display a menu of negation and bitwise operators. • {Neg} ... {negation}*2 • {Not}/{and}/{or}/{xor}/{xnor} ...
2-7-5 Binary, Octal, Decimal, and Hexadecimal Calculations with Integers ○ ○ ○ ○ ○ Example 2 To display the result of “368 or 1110 2” as an octal value u3(SET UP)5(Oct)i Adg2(LOGIC) e(or)1(d~o)d(b) bbbaw ○ ○ ○ ○ ○ Example 3 To negate 2FFFED16 u3(SET UP)3(Hex)i A2(LOGIC)c(Not) cFFFED*1w u Number System Transformation Press 3(DISP) to display a menu of number system transformation functions. • {'Dec}/{'Hex}/{' Bin}/{'Oct} ...
2-8-1 Matrix Calculations 2-8 Matrix Calculations From the Main Menu, enter the RUN • MAT Mode, and press 1(MAT) to perform Matrix calculations. 26 matrix memories (Mat A through Mat Z) plus a Matrix Answer Memory (MatAns), make it possible to perform the following matrix operations.
2-8-2 Matrix Calculations k Inputting and Editing Matrices Pressing 1(MAT) displays the matrix editor screen. Use the matrix editor to input and edit matrices. m × n … m (row) × n (column) matrix None… no matrix preset • {DIM} ... {specifies the matrix dimensions (number of cells)} • {DEL}/{DEL·A} ... deletes {a specific matrix}/{all matrices} u Creating a Matrix To create a matrix, you must first define its dimensions (size) in the Matrix list. Then you can input values into the matrix.
2-8-3 Matrix Calculations u To input cell values ○ ○ ○ ○ ○ Example To input the following data into Matrix B : 1 2 3 4 5 6 c (Selects Mat B.) w bwcwdw ewfwgw (Data is input into the highlighted cell. Each time you press w, the highlighting moves to the next cell to the right.) # You can input complex numbers into the cell of a matrix. # Displayed cell values show positive integers up to six digits, and negative integers up to five digits (one digit used for the negative sign).
2-8-4 Matrix Calculations u Deleting Matrices You can delete either a specific matrix or all matrices in memory. u To delete a specific matrix 1. While the Matrix list is on the display, use f and c to highlight the matrix you want to delete. 2. Press 2(DEL). 3. Press w(Yes) to delete the matrix or i(No) to abort the operation without deleting anything. u To delete all matrices 1. While the Matrix list is on the display, press 3(DEL·A). 2.
2-8-5 Matrix Calculations k Matrix Cell Operations Use the following procedure to prepare a matrix for cell operations. 1. While the Matrix list is on the display, use f and c to highlight the name of the matrix you want to use. You can jump to a specific matrix by inputting the letter that corresponds to the matrix name. Inputting ai(N), for example, jumps to Mat N. Pressing !-(Ans) jumps to the Matrix current Memory. 2. Press w and the function menu with the following items appears. • {EDIT} ...
2-8-6 Matrix Calculations u To calculate the scalar multiplication of a row ○ ○ ○ ○ ○ Example To calculate the product of row 2 of the following matrix and the scalar 4: Matrix A = 1 2 3 4 5 6 2(R-OP)c(×Row) Input multiplier value. ew Specify row number.
2-8-7 Matrix Calculations u To add two rows together ○ ○ ○ ○ ○ Example To add row 2 to row 3 of the following matrix : Matrix A = 1 2 3 4 5 6 2(R-OP)e(Row+) Specify number of row to be added. cw Specify number of row to be added to. dw 6(EXE) (orw) u Row Operations • {R • DEL} ... {delete row} • {R • INS} ... {insert row} • {R • ADD} ...
2-8-8 Matrix Calculations u To insert a row ○ ○ ○ ○ ○ Example To insert a new row between rows one and two of the following matrix : Matrix A = 1 2 3 4 5 6 c 4(R • INS) u To add a row ○ ○ ○ ○ ○ Example To add a new row below row 3 of the following matrix : Matrix A = 1 2 3 4 5 6 cc 5(R • ADD) 20010101
2-8-9 Matrix Calculations u Column Operations • {C • DEL} ... {delete column} • {C • INS} ... {insert column} • {C • ADD} ...
2-8-10 Matrix Calculations u To add a column ○ ○ ○ ○ ○ Example To add a new column to the right of column 2 of the following matrix : Matrix A = 1 2 3 4 5 6 e 6(g)3(C • ADD) k Modifying Matrices Using Matrix Commands [OPTN]-[MAT] u To display the matrix commands 1. From the Main Menu, enter the RUN • MAT Mode. 2. Press K to display the option menu. 3. Press 2(MAT) to display the matrix command menu.
2-8-11 Matrix Calculations u Matrix Data Input Format [OPTN]-[MAT]-[Mat] The following shows the format you should use when inputting data to create a matrix using the Mat command. a11 a12 a21 a22 a1n a2n am1 am2 amn = [ [a11, a12, ..., a1n ] [a21, a22, ..., a2 n] .... [am 1, am2, ...
2-8-12 Matrix Calculations u To input an identity matrix [OPTN]-[MAT]-[Ident] Use the Identity command to create an identity matrix. ○ ○ ○ ○ ○ Example 2 To create a 3 × 3 identity matrix as Matrix A K2(MAT)g(Ident) da2(MAT)b(Mat)av(A)w Number of rows/columns u To check the dimensions of a matrix [OPTN]-[MAT]-[Dim] Use the Dim command to check the dimensions of an existing matrix.
2-8-13 Matrix Calculations u Modifying Matrices Using Matrix Commands You can also use matrix commands to assign values to and recall values from an existing matrix, to fill in all cells of an existing matrix with the same value, to combine two matrices into a single matrix, and to assign the contents of a matrix column to a list file.
2-8-14 Matrix Calculations u To fill a matrix with identical values and to combine two matrices into a single matrix [OPTN]-[MAT]-[Fill]/[Augmnt] Use the Fill command to fill all the cells of an existing matrix with an identical value and the Augment command to combine two existing matrices into a single matrix.
2-8-15 Matrix Calculations u To assign the contents of a matrix column to a list [OPTN]-[MAT]-[M→List] Use the following format with the Mat→List command to specify a column and a list.
2-8-16 Matrix Calculations k Matrix Calculations [OPTN]-[MAT] Use the matrix command menu to perform matrix calculation operations. u To display the matrix commands 1. From the Main Menu, enter the RUN • MAT Mode. 2. Press K to display the option menu. 3. Press 2(MAT) to display the matrix command menu. The following describes only the matrix commands that are used for matrix arithmetic operations. • {Mat} ... {Mat command (matrix specification)} • {Det} ... {Det command (determinant command)} • {Trn} .
2-8-17 Matrix Calculations u Matrix Arithmetic Operations ○ ○ ○ ○ ○ Example 1 [OPTN]-[MAT]-[Mat] To add the following two matrices (Matrix A + Matrix B) : A= 1 1 2 1 B= 2 3 2 1 AK2(MAT)b(Mat)av(A)+ 2(MAT)b(Mat)al(B)w ○ ○ ○ ○ ○ Example 2 Calculate the product to the following matrix using a multiplier value of 5 : Matrix A = 1 2 3 4 AfK2(MAT)b(Mat) av(A)w ○ ○ ○ ○ ○ Example 3 To multiply the two matrices in Example 1 (Matrix A × Matrix B) AK2(MAT)b(Mat)av(A)* 2(MAT)b(Mat)al(B)w ○ ○ ○ ○ ○
2-8-18 Matrix Calculations u Determinant [OPTN]-[MAT]-[Det] ○ ○ ○ ○ ○ Example Obtain the determinant for the following matrix : 1 2 3 4 5 6 –1 –2 0 Matrix A = K2(MAT)d(Det)2(MAT)b(Mat) av(A)w u Matrix Transposition [OPTN]-[MAT]-[Trn] A matrix is transposed when its rows become columns and its columns become rows.
2-8-19 Matrix Calculations u Matrix Inversion [OPTN]-[MAT]-[x –1 ] ○ ○ ○ ○ ○ Example To invert the following matrix : Matrix A = 1 2 3 4 K2(MAT)b(Mat) av(A)!) (x –1) w u Squaring a Matrix ○ ○ ○ ○ ○ Example [OPTN]-[MAT]-[x 2] To square the following matrix : Matrix A = 1 2 3 4 K2(MAT)b(Mat)av(A)xw # Only square matrices (same number of rows and columns) can be inverted. Trying to invert a matrix that is not square produces an error.
2-8-20 Matrix Calculations u Raising a Matrix to a Power [OPTN]-[MAT]-[ ] ○ ○ ○ ○ ○ Example To raise the following matrix to the third power : Matrix A = 1 2 3 4 K2(MAT)b(Mat)av(A) Mdw u Determining the Absolute Value, Integer Part, Fraction Part, and Maximum Integer of a Matrix ○ ○ ○ ○ ○ Example [OPTN]-[NUM]-[Abs]/[Frac]/[Int]/[Intg] To determine the absolute value of the following matrix : Matrix A = 1 –2 –3 4 K5(NUM)b(Abs) K2(MAT)b(Mat)av(A)w # Determinants and inverse matrices are subjec
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