Introduction to Electric Circuits

144 Nodal and mesh analysis

Solution

3 2

A=

5 1

The product of the elements along the diagonal to the right is 3 x 1 = 3.

The product of the elements along the diagonal to the left is 2 • 5 = 10.

Therefore A = 3 - 10 = -7.

Example 7.5

Find the determinant of the 3 • 3 matrix

4I~ 240 il

Solution

A= 4 2 1

2 4 3

5 0 6

The sum of the products of the elements along the diagonals to the right is

(4x4x6)+(2x3x5)+ (1x2x0)=126

The sum of the products of the elements along the diagonals to the left is

(1•215215215215215

Therefore A = 126 - 44 = 82.

It might be found helpful to set out the elements of the determinant again

alongside the original one to see the three diagonals in each direction.

The minor of an element

This is defined as the determinant of the submatrix obtained by deleting the

row and the column containing the element. Thus for the matrix

21 a22 a23|

31 a32 a33.]

the minor of element a21 is

a~2 a13

a32 a33