Sample QuestionsMatrices questions
One sample from each question group in this chapter. Select any group above to see the full set with answer keys.
Given $\left[\begin{array}{cc}2 & 1 \\ -3 & 4\end{array}\right], X=\left[\begin{array}{l}7 \\ 6\end{array}\right]$ the order of the matrix $X$
View full solution →If $\left[\begin{array}{ll}1 & 3 \\ 0 & 0\end{array}\right]\left[\begin{array}{c}2 \\ -1\end{array}\right]=\left[\begin{array}{l}x \\ 0\end{array}\right]$ Find the value of $x$
View full solution →Construct a $2 \times 2$ matrix whose elements $a_{ij}$ are given by $a_{ij} = i.j$
View full solution →Construct a $2 \times 2$ matrix whose elements $a_{ij}$ are given by $a_{ij} = 2i – j$
View full solution →If a matrix has 8 elements, what are the possible order it can have?
If $A=\left[\begin{array}{ll}1 & 2 \\ 2 & 1\end{array}\right]$ and $B=\left[\begin{array}{ll}2 & 1 \\ 1 & 2\end{array}\right]$, fin $A(B A)$
View full solution →Given $A=\left[\begin{array}{ll}1 & 1 \\ 8 & 3\end{array}\right]$, evaluate $A^2-4 A$
View full solution →Solve the matrix equation $: \left[\begin{array}{l}4 \\ 1\end{array}\right], X =\left[\begin{array}{ll}-4 & 8 \\ -1 & 2\end{array}\right]$
View full solution →Let $M \times\left[\begin{array}{ll}1 & 1 \\ 0 & 2\end{array}\right]=\left[\begin{array}{ll}1 & 2\end{array}\right]$ where $M$ is a matrix.
(i) State the order of matrix M
(ii) Find the matrix $M$
View full solution →If $\left[\begin{array}{ll}a & 1 \\ 1 & 0\end{array}\right]\left[\begin{array}{cc}4 & 3 \\ -3 & 2\end{array}\right]=\left[\begin{array}{cc}b & 11 \\ 4 & c\end{array}\right]$ find $a, b$ and $c$
View full solution →If $A =\left[\begin{array}{cc}-1 & 3 \\ 2 & 4\end{array}\right], B =\left[\begin{array}{cc}2 & -3 \\ -4 & -6\end{array}\right]$ find the matrix $A B+B A$
View full solution →Evaluate: $\left[\begin{array}{rr}4 \sin 30^{\circ} & 2 \cos 60^{\circ} \\ \sin 90^{\circ} & 2 \cos 0^{\circ}\end{array}\right]\left[\begin{array}{ll}4 & 5 \\ 5 & 4\end{array}\right]$
View full solution →Given martices $A=\left[\begin{array}{ll}2 & 1 \\ 4 & 2\end{array}\right]$ and $B=\left[\begin{array}{cc}3 & 4 \\ -1 & -2\end{array}\right], C=\left[\begin{array}{cc}-3 & 1 \\ 0 & -2\end{array}\right]$ Find the products of (i) $A B C$ (ii) $A C B$ and state whether they are equal.
View full solution →If $A =\left[\begin{array}{ll}3 & 7 \\ 2 & 4\end{array}\right], B =\left[\begin{array}{ll}0 & 2 \\ 5 & 3\end{array}\right]$ and $C =\left[\begin{array}{cc}1 & -5 \\ -4 & 6\end{array}\right]$ Find $AB -5 C$
View full solution →If $A=\left[\begin{array}{cc}2 & -1 \\ -4 & 5\end{array}\right]$ and $B=\left[\begin{array}{ll}0 & -3\end{array}\right]$ find the matrix $C$ such that $C A=B$
View full solution →If $B=\left[\begin{array}{cc}-4 & 2 \\ 5 & -1\end{array}\right]$ and $C=\left[\begin{array}{cc}17 & -1 \\ 47 & -13\end{array}\right]$ find the matrix $A$ such that $A B=C$
View full solution →If $A=\left[\begin{array}{cc}3 & -4 \\ -1 & 2\end{array}\right]$, find matrix $B$ such that $B A=1$, where $I$ is unity matrix of order 2
View full solution →If $A=\left[\begin{array}{cc}2 & -1 \\ -4 & 5\end{array}\right]$ and $B=\left[\begin{array}{c}-3 \\ 2\end{array}\right]$ find the matrix $C$ such that $A C=B$
View full solution →$A=\left[\begin{array}{ll}1 & 0 \\ 2 & 1\end{array}\right]$ and $B=\left[\begin{array}{cc}2 & 3 \\ -1 & 0\end{array}\right]$ Find $A^2+A B+B^2$
View full solution →Find the values of $a, b, c$ and $d$ if $\left[\begin{array}{ll}a+b & 3 \\ 5+c & a b\end{array}\right]=\left[\begin{array}{cc}6 & d \\ -1 & 8\end{array}\right]$
View full solution →Find the matrix $B$ if $A=\left[\begin{array}{ll}4 & 1 \\ 2 & 3\end{array}\right]$ and $A^2=A+2 B$
View full solution →If $B=\left[\begin{array}{cc}-4 & 2 \\ 5 & -1\end{array}\right]$ and $C=\left[\begin{array}{cc}17 & -1 \\ 47 & -13\end{array}\right]$ find the matrix $A$ such that $A B=C$
View full solution →$A=\left[\begin{array}{ll}1 & 0 \\ 0 & 1\end{array}\right]$ then $A^2=$
- A
$\left[\begin{array}{ll}1 & 1 \\ 0 & 0\end{array}\right]$
- B
$\left[\begin{array}{ll}0 & 0 \\ 1 & 1\end{array}\right]$
- ✓
$\left[\begin{array}{ll}1 & 0 \\ 0 & 1\end{array}\right]$
- D
$\left[\begin{array}{ll}0 & 1 \\ 1 & 0\end{array}\right]$
Answer: C.
View full solution →If $A+B=\left[\begin{array}{ll}1 & 0 \\ 1 & 1\end{array}\right]$ and $A-2 B=\left[\begin{array}{cc}-1 & 1 \\ 0 & -1\end{array}\right]$ then $A$ is equal to
- A
$\frac{1}{3}\left[\begin{array}{ll}1 & 1 \\ 2 & 1\end{array}\right]$
- B
$\frac{1}{3}\left[\begin{array}{ll}2 & 1 \\ 1 & 2\end{array}\right]$
- ✓
$\left[\begin{array}{ll}1 & 1 \\ 2 & 1\end{array}\right]$
- D
$\left[\begin{array}{ll}2 & 1 \\ 1 & 2\end{array}\right]$
Answer: C.
View full solution →If $B=\left[\begin{array}{ll}1 & 5 \\ 0 & 3\end{array}\right]$ and $A-2 B=\left[\begin{array}{cc}0 & 4 \\ -7 & 5\end{array}\right]$ then the matrix $A$ is equal to
- A
$\left[\begin{array}{cc}2 & 14 \\ -7 & 11\end{array}\right]$
- B
$\left[\begin{array}{cc}-2 & 14 \\ 7 & 11\end{array}\right]$
- C
$\left[\begin{array}{cc}2 & -14 \\ 7 & 11\end{array}\right]$
- ✓
$\left[\begin{array}{ll}-2 & 14 \\ -7 & 11\end{array}\right]$
Answer: D.
View full solution →If $x \begin{bmatrix} 2 \\ 3\end{bmatrix} +y \begin{bmatrix} -1 \\ 0 \end{bmatrix} = \begin{bmatrix} 10 \\ 6\end{bmatrix} $ then the values of $x$ and $y$ are
- A
$x=2, y=6$
- ✓
$x=2, y=-6$
- C
$x=3, y=-4$
- D
$x=3, y=-6$
Answer: B.
View full solution →If $\left[\begin{array}{cc}x+2 y & 3 y \\ 4 x & 2\end{array}\right]=\left[\begin{array}{cc}0 & -3 \\ 8 & 2\end{array}\right]$ then the value of $x-y$ is
Answer: C.
View full solution →