94
Example Obtain the determinant for the following matrix :
123
Matrix A = 456
–1 –2 0
3(Det)1(Mat)aAw
•Determinants can be obtained only for square matrices (same number of rows
and columns). Trying to obtain a determinant for a matrix that is not square
produces an error.
• The determinant of a 2 × 2 matrix is calculated as shown below.
| A | =
a11 a12
= a11a22 – a12a21
a21 a22
• The determinant of a 3 × 3 matrix is calculated as shown below.
a11 a12 a13
| A | = a21 a22 a23
a31 a32 a33
= a11a22a33 + a12a23a31 + a13a21a32
– a11a23a32 – a12a21a33 – a13a22a31
kk
kk
k Matrix Transposition
A matrix is transposed when its rows become columns and its columns become
rows. The following is the format for matrix transposition.
Matrix
Mat A
4 (Trn) w
Mat Z
MatAns
Example To transpose the following matrix :
12
Matrix A = 34
56
4(Trn)1(Mat)aAw
6 - 4 Matrix Calculations
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