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

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

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

Which of the following matrix has no inverse.

If A = \(\begin{vmatrix}cos \theta & sin \theta \\ -sin \theta&cons\theta \end{vmatrix},\) then |2A| is equal to ________.

The technology matrix of an economic system of two industries is\(\begin{bmatrix} 0.50 & 0.30 \\ 0.41 & 0.33 \end{bmatrix}\). Test whether the system is viable as per Hawkins Simon conditions.

The technology matrix of an economic system of two industries is\(\begin{bmatrix} 0.6 & 0.9 \\ 0.20 & 0.80 \end{bmatrix}\) .Test whether the system is viable as per Hawkins-Simon conditions.

Solve:\(\begin{vmatrix}7&4&11\\-3&5&x\\-x&3&1 \end{vmatrix}=0\)

Using the property of determinant, evaluate \(\begin{vmatrix} 6 &5 &12 \\ 2 & 4 &4 \\2 & 1 & 4 \end{vmatrix}.\)

Evaluate: \(\left| \begin{matrix} 1 & 2 & 4 \\ -1 & 3 & 0 \\ 4 & 1 & 0 \end{matrix} \right| \)

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

If A \(= \begin{bmatrix} 1 & -1 \\2 & 3 \end{bmatrix}\) show that A² - 4A + 5I₂ = 0 and also find A^-1.

Using matrix method, solve x + 2y + z = 7, x + 3z = 11 and 2x - 3y =1.

Write the minors and co-factors of the elements of \(\begin{vmatrix}5 & 3 \\-6 & 2\end{vmatrix}\)

Solve: 2x + 5y = 1 and 3x + 2y = 7 using matrix method.

Evaluate:\(\begin{vmatrix} 1&a&a^2-bc\\1&b&b^2-ca\\1&c&c^2-ab \end{vmatrix}\)

Solve by using matrix inversion method: x - y + z = 2; 2x - y = 0 , 2y - z = 1.

If \(A=\left[ \begin{matrix} 1 & tan\quad x \\ -tan\quad x & \quad \quad \quad 1 \end{matrix} \right] \), then show that A^TA^-1 = \(\left[ \begin{matrix} cos\quad 2x & -sin2x \\ sin\quad 2x & cos2x \end{matrix} \right] .\)

Two types of radio values A, B are available and two types of radios P and Q are assembled in a small factory. The factory uses 2 valves of type A and 3 valves of type B for the type B for the type of radio P, and for the radio Q it uses 3 valves of type A and 4 valves of type B. If the number of valves of type A and B used by the factory are 130 and 180 respectively, find out the number of radios assembled use matrix method.