List of top Mathematics Questions on Matrices asked in CBSE CLASS XII

If $A = \begin{bmatrix} 1 & 2 & 2 \\ 2 & 1 & 2 \\ 2 & 2 & 1 \end{bmatrix}$, then compute $A^2 - 4A - 5I$.

Find the cost (per kg) of each fertilizer A, B and C that a farmer needs to buy, such that 1 kg each of fertilizer A and C added to 2 kg of B costs him ₹ 400. Also, the cost of each kg of fertilizer B and C added together is equal to the cost of 1 kg of fertilizer A. However, the cost of 3 kg of fertilizer B added to ₹ 200 is the same as the cost of 1 kg of fertilizer A and C together. Use the matrix method to find the solution.

If \( A \) is a non-singular matrix, then which of the following is not true ?

If \( A = \begin{bmatrix} \sin \theta & \cos \theta \\ -\cos \theta & \sin \theta \end{bmatrix} \) and \( A + A' = I \), then \( \theta \) is equal to :

If \( A \) is a symmetric matrix, then for any matrix \( B \) of order same as \( A \), \( BAB' \) is a/an :

Let \( A = \begin{bmatrix} 0 & -3 & 4 \\ 1 & 0 & 2 \end{bmatrix} \) and \( B = \begin{bmatrix} -3 & 0 & 1\\ 2 & 4 & 0 \end{bmatrix} \). If \( A + B + C = O \), then matrix \( C \) is :

If \[ P= \begin{bmatrix} 0 & 1 & 2\\ 2 & 3 & 4\\ 1 & -1 & 0 \end{bmatrix} \] and \[ Q= \begin{bmatrix} 2 & -1 & 5\\ -4 & 2 & -4\\ 2 & 2 & -4 \end{bmatrix}, \] find the matrix product \[ QP. \] Hence, solve the following system of linear equations using matrices: \[ x-y=3,\qquad 2x+3y+4z=17,\qquad y+2z=7. \]

Given that $P = \begin{bmatrix} 2 & -1 \\ 3 & 4 \end{bmatrix}$, $Q = \begin{bmatrix} 5 & 2 \\ 7 & 4 \end{bmatrix}$ and $R = \begin{bmatrix} 2 & 5 \\ 3 & 8 \end{bmatrix}$, find a matrix $S$ such that $PQ - RS$ is a null matrix.

If \[ P = \begin{bmatrix} 1 & -1 & 0 \\ 2 & 3 & 4 \\ 0 & 1 & 2 \end{bmatrix} \quad \text{and} \quad Q = \begin{bmatrix} 2 & 2 & -4 \\ -4 & 2 & -4 \\ 1 & -1 & 5 \end{bmatrix} \] find \( QP \) and hence solve the following system of equations using matrix method:
\[ x - y = 3,\quad 2x + 3y + 4z = 13,\quad y + 2z = 7 \]

If \[ A = \begin{bmatrix} \frac{1}{2}\cos x & -\sin x \\ \sin x & \frac{1}{2}\cos x \end{bmatrix} \] and \(A + A^T = I\), then the value of \(x \in \left[-\frac{\pi}{2}, \frac{\pi}{2}\right]\) is

If $A$ and $B$ are square matrices of same order, then which of the following statements is/are always true?
(i) $(A+B)(A-B)=A^2-B^2$
(ii) $AB=BA$
(iii) $(A+B)^2=A^2+AB+BA+B^2$
(iv) $AB=0 \Rightarrow A=0$ or $B=0$