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

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

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 ________.

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

adj (AB) is equal to ________.

The inventor of input-output analysis is ________.

The inverse matrix of \(\begin{pmatrix} 3 & 1 \\ 5 & 2\end{pmatrix}\) is ________.

If A \(=\begin{pmatrix} -1 & 2 \\ 1 & -4 \end{pmatrix}\) then A (adj A) is ________.

The value of \(\begin{vmatrix} 5 & 5 & 5 \\ 4x & 4y & 4z \\ -3x & -3y & -3z \end{vmatrix}\)is ________.

If A is 3 \(\times\) 3 matrix and |A| = 4, then |A^-1| is equal to ________.

Find the adjoint of the matrix \(A=\begin{bmatrix}2&3\\1&4 \end{bmatrix}\)

Find the inverse of each of the following matrices.\(\left[\begin{array}{rr} 1 & -1 \\ 2 & 3 \end{array}\right]\)

Solve\(\left| \begin{matrix} x-1 & x & x-2 \\ 0 & x-2 & x-3 \\ 0 & 0 & x-3 \end{matrix} \right| =0\)

Evaluate\(\left| \begin{matrix} 1 & 3 & 4 \\ 102 & 18 & 36 \\ 17 & 3 & 6 \end{matrix} \right| \)

Show that \(\left[ \begin{matrix} 1 & 2 \\ 2 & 4 \end{matrix} \right] \)is a singular matrix.

Evaluate: \(\begin{bmatrix} 3&-2&4\\2&0&1\\1&2&3 \end{bmatrix}\)

Find |AB| if \(A=\begin{bmatrix} 3&-1\\2&1 \end{bmatrix} \) and \(B =\begin{bmatrix} 3&0\\1&-2 \end{bmatrix}\)

Show that \(\begin{vmatrix}0 &ab^2 &ac^2 \\a^2b & 0 & bc^2\\a^2c&b^2c&0\end{vmatrix}=2a^3b^3c^3.\)

Solve by matrix inversion method: 2x + 3y - 5 = 0, x - 2y + 1 = 0.

If \(A=\left[\begin{array}{rr} 2 & 3 \\ 1 & -6 \end{array}\right] \text { and } B=\left[\begin{array}{rr} -1 & 4 \\ 1 & -2 \end{array}\right],\) then verify adj (AB) = (adj B) (adj A).

You are given the following transaction matrix for a two sector economy.

i) Write the technology matrix.
ii) Determine the output when the final demand for the output sector 1 alone increases to 23 units.

If A = \(\begin{bmatrix}1 & 1 & 1 \\ 3 & 4 & 7\\1 & -1 & 1 \end{bmatrix}\) verify that A ( adj A ) = ( adj A ) A = |A| I₃.

If A = \(\begin{bmatrix}3 & -1 & 1 \\ -15 & 6 & -5\\5 & -2 & 2 \end{bmatrix}\) then, find the Inverse of A.

If A =\(\left[ \begin{matrix} -1 & 2 & -2 \\ 4 & -3 & 4 \\ 4 & -4 & 5 \end{matrix} \right] \)then, show that the inverse of A is A itself.

Solve by matrix inversion method: x - y + 2z = 3; 2x + z = 1; 3x + 2y + z = 4.