Find the determinants of the following matrices 2 1 0 1 0 1

Find the determinants of the following matrices.

Solution

a)

Your matrix

Swap the 1st and the 2nd rows inversing determinant sign

Eliminate elements in the 1st column under the 1st element

Eliminate elements in the 2nd column under the 2nd element

Multiply the main diagonal elements

-(1 x 2 x (-1/2) x 1) = 1

solution

Determinant is 1

b)

Your matrix

Eliminate elements in the 1st column under the 1st element

Eliminate elements in the 2nd column under the 2nd element

Multiply the main diagonal elements

4 x 9/2 x 0 = 0

solution

Determinant is 0

c)

Your matrix

Multiply the main diagonal elements

1 x 2 x 9 x (-1) = -18

solution

Determinant is -18