The value of x if \(\begin{vmatrix} 0 & 1 & 0 \\ x & 2 & x \\ 1 & 3 & x \end{vmatrix}=0\) is_________.

(a)

0, - 1

(b)

0, 1

(c)

- 1, 1

(d)

- 1, - 1

The value of \(\begin{vmatrix} 2x+y & x & y \\ 2y+z & y & z \\ 2z+x & z & x \end{vmatrix}\) is ________.

(a)

xyz

(b)

x+y+z

(c)

2x+2y+2z

(d)

0

The co-factor of -7 in the determinant \(\begin{vmatrix} 2 & -3 & 5 \\ 6 & 0 & 4 \\ 1 & 5 & -7 \end{vmatrix}\) is________.

(a)

-18

(b)

18

(c)

-7

(d)

7

If \(\triangle=\begin{vmatrix} 1 & 2 & 3 \\ 3 & 1 & 2 \\ 2 & 3 & 1 \end{vmatrix}\) then \(\begin{vmatrix} 3 & 1 & 2 \\ 1 & 2 & 3 \\ 2 & 3 & 1 \end{vmatrix}\) is ________.

(a)

\(\triangle\)

(b)

-\(\triangle\)

(c)

3\(\triangle\)

(d)

-3\(\triangle\)

The value of the determinant \({\begin{vmatrix} a & 0 & 0 \\ 0 & a & 0 \\ 0 & 0 & c \end{vmatrix}}^{2}\)is ________.

(a)

abc

(b)

0

(c)

a²b²c²

(d)

-abc

If A is square matrix of order 3, then |kA| is________.

(a)

k|A|

(b)

-k|A|

(c)

k³|A|

(d)

-k³|A|

adj (AB) is equal to ________.

(a)

adj A adj B

(b)

adj A^T adj B^T

(c)

adj B adj A

(d)

adj B^T adj A^T

The inverse matrix of \(\begin{pmatrix} \frac { 1 }{ 5 } & \frac { 5 }{ 25 } \\ \frac { 2 }{ 5 } & \frac { 1 }{ 2 } \end{pmatrix}\) is ________.

(a)

\({{7}\over{30}}\begin{pmatrix} \frac { 1 }{ 2 } & \frac { 5 }{ 12 } \\ \frac { 2 }{ 5 } & \frac { 4 }{ 5 } \end{pmatrix}\)

(b)

\({{7}\over{30}}\begin{pmatrix} \frac { 1 }{ 2 } & \frac { -5 }{ 12 } \\ \frac { -2 }{ 5 } & \frac { 1 }{ 5 } \end{pmatrix}\)

(c)

\({{30}\over{7}}\begin{pmatrix} \frac { 1 }{ 2 } & \frac { 5 }{ 12 } \\ \frac { 2 }{ 5 } & \frac { 4 }{ 5 } \end{pmatrix}\)

(d)

\({{30}\over{7}}\begin{pmatrix} \frac { 1 }{ 2 } & \frac { -5 }{ 12 } \\ \frac { -2 }{ 5 } & \frac { 4 }{ 5 } \end{pmatrix}\)

If A = \(\begin{pmatrix} a & b \\ c & d \end{pmatrix}\)such that ad - bc \(\neq\) 0 then A^-1 is ________.

(a)

\({{1}\over{ad-bc}}\begin{pmatrix} d & b \\-c & a\end{pmatrix}\)

(b)

\({{1}\over{ad-bc}}\begin{pmatrix} d & b \\c & a\end{pmatrix}\)

(c)

\({{1}\over{ad-bc}}\begin{pmatrix} d & -b \\-c & a\end{pmatrix}\)

(d)

\({{1}\over{ad-bc}}\begin{pmatrix} d & -b \\c & a\end{pmatrix}\)

The number of Hawkins-Simon conditions for the viability of an input - output analysis is ________.

(a)

1

(b)

3

(c)

4

(d)

2