Sample QuestionsMatrices questions
One sample from each question group in this chapter. Select any group above to see the full set with answer keys.
Evaluate: $\left[\begin{array}{cc}4 \sin 30^{\circ} & 2 \cos 60^{\circ} \\ \sin 90^{\circ} & 2 \cos 0^{\circ}\end{array}\right]\left[\begin{array}{ll}4 & 5 \\ 5 & 4\end{array}\right]$.
View full solution →If $A =\left[\begin{array}{cc}3 & -2 \\ -1 & 4\end{array}\right], B =\left[\begin{array}{l}6 \\ 1\end{array}\right], C =\left[\begin{array}{r}-4 \\ 5\end{array}\right]$ and $D =\left[\begin{array}{l}2 \\ 2\end{array}\right]$, find $AB +2 C -4 D$.
View full solution →Find $x$ and $y$ if $\left[\begin{array}{cc}2 x & x \\ y & 3 y\end{array}\right]\left[\begin{array}{l}3 \\ 2\end{array}\right]=\left[\begin{array}{l}16 \\ 9\end{array}\right]$.
View full solution →If $A =\left[\begin{array}{cc}p & 0 \\ 0 & 2\end{array}\right], B =\left[\begin{array}{cc}0 & -q \\ 1 & 0\end{array}\right]$ and $C =\left[\begin{array}{cc}2 & -2 \\ 2 & 2\end{array}\right]$ and $BC = C ^2$, find the values of $p$ and $q$.
View full solution →If $\left[\begin{array}{cc}1 & 4 \\ -2 & 3\end{array}\right]+2 M=3\left[\begin{array}{cc}3 & 2 \\ 0 & -3\end{array}\right]$, find the matrix $M$.
View full solution →If $A=\left[\begin{array}{ll}3 & 0 \\ 5 & 1\end{array}\right]$ and $B=\left[\begin{array}{cc}-4 & 2 \\ 1 & 0\end{array}\right]$, find $A^2-2 A B+B^2$.
View full solution →Given $\left[\begin{array}{cc}4 & 2 \\ -1 & 1\end{array}\right] M =6 I$, where $M$ is a matrix and $I$ is unit matrix of order $2 \times 2$.
(a) State the order of matrix M.
(b) Find the matrix M.
View full solution →If $A=\left[\begin{array}{ll}2 & 3 \\ 5 & 7\end{array}\right], B=\left[\begin{array}{cc}0 & 4 \\ -1 & 7\end{array}\right]$ and $C=\left[\begin{array}{cc}1 & 0 \\ -1 & 4\end{array}\right]$, find $A C+B^2-10 C$.
View full solution →Given matrix $B=\left[\begin{array}{ll}1 & 1 \\ 8 & 3\end{array}\right]$. Find the matrix $X$ if, $X=B^2-4 B$. Hence solve for $a$ and $b$ given $X \left[\begin{array}{l}a \\ b\end{array}\right]=\left[\begin{array}{c}5 \\ 50\end{array}\right]$
View full solution →If $A=\left[\begin{array}{ll}1 & 3 \\ 3 & 4\end{array}\right]$ and $B=\left[\begin{array}{ll}-2 & 1 \\ -3 & 2\end{array}\right]$ and $A^2-5 B^2=5 C$, find matrix $C$, where $C$ is a 2 by 2 matrix.
View full solution →If $A =\left[\begin{array}{ll}x & 3 \\ y & 3\end{array}\right]$ and $A ^2=3 I$, where $I =\left[\begin{array}{ll}1 & 0 \\ 0 & 1\end{array}\right]$ the order of $A ^2$ is :
- A
$2 \times 2$
- B
$2 \times 3$
- C
$1 \times 2$
- D
$3 \times 2$
View full solution →If $A=\left[\begin{array}{cc}2 & 0 \\ -3 & 1\end{array}\right], B=\left[\begin{array}{cc}0 & 1 \\ -2 & 3\end{array}\right]$, then the matrix $B A$ is :
- A
$\left[\begin{array}{cc}-3 & 1 \\ -13 & 3\end{array}\right]$
- B
$\left[\begin{array}{ll}-4 & 5 \\ -2 & 7\end{array}\right]$
- C
$\left[\begin{array}{cc}-3 & 2 \\ 5 & -7\end{array}\right]$
- D
$\left[\begin{array}{cc}4 & -1 \\ 2 & 19\end{array}\right]$
View full solution →If $A =\left[\begin{array}{ll}1 & 2 \\ 3 & 3\end{array}\right], B =\left[\begin{array}{ll}x & 0 \\ 0 & y\end{array}\right]$, then the order of the matrix BA is :
- A
$1 \times 2$
- B
$2 \times 1$
- C
$2 \times 3$
- D
$2 \times 2$
View full solution →If $A=\left[\begin{array}{cc}2 & 1 \\ -1 & 4\end{array}\right], B=\left[\begin{array}{cc}5 & -1 \\ 2 & -1\end{array}\right]$, then $A^T-B^T$ is equal to :
- A
$\left[\begin{array}{cc}1 & -1 \\ 4 & 2\end{array}\right]$
- B
$\left[\begin{array}{cc}7 & -1 \\ 2 & 5\end{array}\right]$
- C
$\left[\begin{array}{cc}-3 & -1 \\ 2 & 4\end{array}\right]$
- D
$\left[\begin{array}{cc}-3 & -3 \\ 2 & 5\end{array}\right]$
View full solution →If $A=\left[\begin{array}{cc}-2 & 3 \\ 4 & 5\end{array}\right], B=\left[\begin{array}{cc}5 & 2 \\ -7 & 3\end{array}\right]$, then transpose of matrix $(A+B)$ is :
- A
$\left[\begin{array}{cc}3 & 5 \\ -3 & 8\end{array}\right]$
- B
$\left[\begin{array}{cc}3 & -3 \\ 5 & 8\end{array}\right]$
- C
$\left[\begin{array}{cc}3 & 8 \\ -3 & 5\end{array}\right]$
- D
$\left[\begin{array}{cc}3 & 5 \\ -8 & 3\end{array}\right]$
View full solution →Assertion (A) : $\left[\begin{array}{lll}2 & 0 & 0 \\ 0 & 5 & 0 \\ 0 & 0 & 1\end{array}\right]$ and $\left[\begin{array}{lll}0 & 0 & 4 \\ 0 & 2 & 0 \\ 8 & 0 & 0\end{array}\right]$ are diagonal matrices.
Reason (R) : Every identity matrix is a diagonal matrix.
View full solution →Assertion (A) : For any two matrices $A$ and $B , A + B = B + A$.
Reason (R) : Multiplication of matrices is not commutative.
View full solution →Assertion (A) : We can always find the product of a matrix and its transpose.
Reason (R) : We can always multiply two matrices of the same order.
Assertion (A) : A row matrix and a column matrix cannot be added.
Reason (R) : We can only add two matrices of the same order.