If \(\left[ \begin{matrix} x & +3y & y \\ 7 & -x & 4 \end{matrix} \right] \)=\(\begin{bmatrix} 4 & -1 \\ 0 & 4 \end{bmatrix}\), find the values of x and y.

If matrix A = \([\begin{matrix} 1 & 2 & 3 \end{matrix}]\) write AA' , where A' is the transpose of matrix A.

If \(\left[ \begin{matrix} y & +2x & 5 \\ & -x & 3 \end{matrix} \right] =\begin{bmatrix} 7 & 5 \\ -2 & 3 \end{bmatrix}\), find the value of y.

If \(A=\left[ { a }_{ ij } \right] =\left[ \begin{matrix} 2 & 3 & -5 \\ 1 & 4 & 9 \\ 0 & 7 & -2 \end{matrix} \right] andb=\left[ { b }_{ ij } \right] =\left[ \begin{matrix} 2 & 1 & -1 \\ -3 & 4 & 4 \\ 1 & 5 & 2 \end{matrix} \right] ,then\quad find\quad { a }_{ 22 }+{ b }_{ 21 }.\)

If \(\begin{bmatrix} 1 & 2 \\ 3 & 4 \end{bmatrix}\begin{bmatrix} 3 & 1 \\ 2 & 5 \end{bmatrix}=\begin{bmatrix} 7 & 11 \\ k & 23 \end{bmatrix}\), find the value of k.

If A and B are invertible matrices of the same order, then (AB)^–1 = B^–1 A^–1.

Let A = [a_ij]be a matric of order 2 x 3 and a_ij = \(\frac { i-j }{ i+j } \), write the value of a₂₃

if \(\left[ \begin{matrix} a+b & 2 \\ 5 & ab \end{matrix} \right] =\left[ \begin{matrix} 6 & 2 \\ 5 & 8 \end{matrix} \right] \)find the relation between a and b 

It is possible to have the product of  two matrices to be the null matrix.
While neither of them is the null matrix? if it is so, give an example

Write the order of matrix B if any matrix of order m x n such that AB and BA both are defined

If \(A=\left[ \begin{matrix} 1 & 4 \\ 3 & 2 \\ 2 & 1 \end{matrix} \right] B=\left[ \begin{matrix} 5 & 2 \\ -1 & 0 \\ 1 & 1 \end{matrix} \right] \), then find the matrix X for which A + B - X = 0.

Solve the matrix equation \(\left[ \begin{matrix} { x }^{ 2 } \\ { y }^{ 2 } \end{matrix} \right] -3\left[ \begin{matrix} x \\ 2y \end{matrix} \right] =\left[ \begin{matrix} -2 \\ -9 \end{matrix} \right] \)

Find the value of X and Y if
\(X+Y=\left[ \begin{matrix} 2 & 3 \\ 5 & 1 \end{matrix} \right] ,X-Y=\left[ \begin{matrix} 6 & 5 \\ 7 & 3 \end{matrix} \right] \)

If a matrix has 24 elements, what are the possible orders it can have? What, if it has 13 elements?

If a matrix has 18 elements, what are the possible orders it can have? What, if it has 5 elements?

If \(A=\left[ \begin{matrix} 3 & 1 & -1 \\ 0 & 1 & 2 \end{matrix} \right] \) , then show that \(AA\prime \) is a symmetric matrix.

Show that: \(\left[ \left( \begin{matrix} 1 & \omega & { \omega }^{ 2 } \\ \omega & { \omega }^{ 2 } & 1 \\ { \omega }^{ 2 } & 1 & \omega \end{matrix} \right) +\left( \begin{matrix} \omega & { \omega }^{ 2 } & 1 \\ { \omega }^{ 2 } & 1 & \omega \\ \omega & { \omega }^{ 2 } & 1 \end{matrix} \right) \right] \left[ \begin{matrix} 1 \\ \omega \\ { \omega }^{ 2 } \end{matrix} \right] =\left[ \begin{matrix} 0 \\ 0 \\ 0 \end{matrix} \right] ,\) where \(\omega \) is a cube root of unity.

If \(A=\left[ \begin{matrix} 1 & 2 & 2 \\ 2 & 1 & 2 \\ 2 & 2 & 1 \end{matrix} \right] \), verify that \({ A }^{ 2 }-4A-5l=0\)

Obtain the inverse of the following matrix, using elementary operations : \(A=\left[ \begin{matrix} 3 & 0 & -1 \\ 2 & 3 & 0 \\ 0 & 4 & 1 \end{matrix} \right] \)

Find matrix A such that 2A - 3B + 5C = 0 Where \(B=\left[ \begin{matrix} -2 & 2 & 0 \\ 3 & 1 & 4 \end{matrix} \right] \)\(C=\left[ \begin{matrix} 2 & 0 & -2 \\ 7 & 1 & 6 \end{matrix} \right] \)

Find the values of x and y for which the following matrix equation A-3B = C is satisfied, where \(A=\left[ \begin{matrix} { x }^{ 2 } \\ { y }^{ 2 } \end{matrix} \right] \), \(B=\left[ \begin{matrix} x \\ 2y \end{matrix} \right] \),\(c=\left[ \begin{matrix} -2 \\ 9 \end{matrix} \right] \)

Let f(x) = x² - 5x+6 find f(A) If, A =\(\left[ \begin{matrix} 2 & 0 & 1 \\ 2 & 1 & 3 \\ 1 & -1 & 0 \end{matrix} \right] \)

A shopkeeper has 3 varieties of pen 'A' , 'B' and 'C'. Meenu purchase 1 pen of each variety for a total of Rs. 21. Jeevan purchase 4 pens of 'A' variety, 3 pen say 'B' variety and 2 pens of 'C' variety for Rs. 60. While Shikha purchased 6 pens of 'A' variety, 2 pens of 'B' variety and 3 pens of 'C' variety for Rs. 70. Using matrix method, find cost of each variety of pen.

If \(A=\left( \begin{matrix} 1 & 3 & 2 \\ 2 & 0 & -1 \\ 1 & 2 & 3 \end{matrix} \right) \), then show that A³ - 4A² - 3A + 11I = 0