hp 49g+_user's guide_English_E_DCVL5300427_V2

Page 11-11

where the values d

are constant, we say that c

is linearly dependent on the

columns included in the summation. (Notice that the values of j include any

value in the set {1, 2, …, n}, in any combination, as long as j≠k.) If the

expression shown above cannot be written for any of the column vectors then

we say that all the columns are linearly independent. A similar definition for

the linear independence of rows can be developed by writing the matrix as a

column of row vectors. Thus, if we find that rank(A) = n, then the matrix has

an inverse and it is a non-singular matrix. If, on the other hand, rank(A) < n,

then the matrix is singular and no inverse exist.

For example, try finding the rank for the matrix:

You will find that the rank is 2. That is because the second row [2,4,6] is

equal to the first row [1,2,3] multiplied by 2, thus, row two is linearly

dependent of row 1 and the maximum number of linearly independent rows is

2. You can check that the maximum number of linearly independent columns

is 3. The rank being the maximum number of linearly independent rows or

columns becomes 2 for this case.

Function DET

Function DET calculates the determinant of a square matrix. For example,