Question

Evaluate the determinants (i) (iii) (ii) (iv)

Answer 1

(i)

The given matrix is,

[ 3 −1 −2 0 0 −1 3 −5 0 ]

Determinant of the given matrix is,

| 3 −1 −2 0 0 −1 3 −5 0 | =3| 0 −1 −5 0 |−( −1 )| 0 −1 3 0 |+( −2 )| 0 0 3 −5 | =3( 0×0−( −1 )×( −5 ) )+1( 0+3 )−2( 0×( −5 )−0×3 ) =−12

Thus, the value of the determinant is −12.

(ii)

The given matrix is,

[ 3 −4 5 1 1 −2 2 3 1 ]

Determinant of the given matrix is,

| 3 −4 5 1 1 −2 2 3 1 | =3| 1 −2 3 1 |−( −4 )| 1 −2 2 1 |+5| 1 1 2 3 | =3( 1×1−( −2 )×( 3 ) )+4( 1−( −2 )×2 )−5( 1×( 3 )−1×2 ) =46

Thus, the value of the determinant is 46.

(iii)

The given matrix is,

[ 0 1 2 −1 0 −3 −2 3 0 ]

Determinant of the given matrix is,

| 0 1 2 −1 0 −3 −2 3 0 | =0| 0 −3 3 0 |−( 1 )| −1 −3 −2 0 |+( 2 )| −1 0 −2 3 | =0( 0×0−( −3 )×( 3 ) )−1( 0−6 )−2( 3×( −1 )−0×( −2 ) ) =0

Thus, the value of determinant is 0.

(iv)

The given matrix is,

[ 2 −1 −2 0 2 −1 3 −5 0 ]

Determinant of the given matrix is,

| 2 −1 −2 0 2 −1 3 −5 0 | =2| 2 −1 −5 0 |−( −1 )| 0 −1 3 0 |+( −2 )| 0 2 3 −5 | =2( 2×0−( −1 )×( −5 ) )+1( 0+3 )−2( 0×( −5 )−3×( 2 ) ) =5

Thus, the value of the determinant is 5.