Sample QuestionsMatrices questions
One sample from each question group in this chapter. Select any group above to see the full set with answer keys.
Find $x$ and $y,$ if $\left[\begin{array}{cc}-3 & 2 \\ 0 & -5\end{array}\right]\left[\begin{array}{l}x \\ 2\end{array}\right] =\left[\begin{array}{c}-5 \\ y\end{array}\right]$
View full solution →If $A = \left[\begin{array}{ll}2 & 4 \\ 3 & 2\end{array}\right]$ and $B = \left[\begin{array}{cc}1 & 3 \\ -2 & 5\end{array}\right]$ find $BA$.
View full solution →If $A=\left[\begin{array}{ll}2 & 4 \\ 3 & 2\end{array}\right]$ and $B=\left[\begin{array}{cc}1 & 3 \\ -2 & 5\end{array}\right]$ find $AB.$
View full solution →Find $x$ and $y,$ if $\left(\begin{array}{ll}x & 3 x \\ y & 4 y\end{array}\right)\left(\begin{array}{l}2 \\ 1\end{array}\right)=\left(\begin{array}{c}5 \\ 12\end{array}\right)$.
View full solution →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 $A =\left[\begin{array}{ll}a & b \\ c & d\end{array}\right]$ and $I =\left[\begin{array}{ll}1 & 0 \\ 0 & 1\end{array}\right]$ show that $A^2 - (a + d) A = (bc - ad) I.$
View full solution →Find $X$ and $Y,$ if $\left[\begin{array}{cc}2 x & x \\ y & 3 y\end{array}\right]\left[\begin{array}{l}3 \\ 2\end{array}\right]=\left[\begin{array}{c}16 \\ 9\end{array}\right]$
View full solution →Given that $A =\left[\begin{array}{ll}3 & 0 \\ 0 & 4\end{array}\right]$ and $B = \left[\begin{array}{ll}a & b \\ 0 & c\end{array}\right]$ and that $AB = A + B,$ find the values of $a, b$ and $c.$
View full solution →Find $x, y$ if $\left[\begin{array}{cc}-2 & 0 \\ 3 & 1\end{array}\right]\left[\begin{array}{c}-1 \\ 2 x\end{array}\right]+3\left[\begin{array}{c}-2 \\ 1\end{array}\right]=2\left[\begin{array}{l}y \\ 3\end{array}\right]$.
View full solution →Given $A = \left[\begin{array}{ll}p & 0 \\ 0 & 2\end{array}\right], B =\left[\begin{array}{cc}0 & -q \\ 1 & 0\end{array}\right], C =\left[\begin{array}{cc}2 & -2 \\ 2 & 2\end{array}\right]$ and $BA = C^2.$ Find the values of $p$ and $q.$
View full solution →Find the value of p and q if:
$\left[\begin{array}{cc}2 p+1 & q^2-2 \\ 6 & 0\end{array}\right]=\left[\begin{array}{cc}p+3 & 3 q-4 \\ 5 q-q^2 & 0\end{array}\right]$.
View full solution →Given $A=\left[\begin{array}{ll}1 & 1 \\ 8 & 3\end{array}\right]$ evaluate $A^2- 4A.$
View full solution →Evaluate $x,y$ if $\left[\begin{array}{cc}3 & -2 \\ -1 & 4\end{array}\right]\left[\begin{array}{c}2 x \\ 1\end{array}\right]+2\left[\begin{array}{c}-4 \\ 5\end{array}\right]=\left[\begin{array}{c}8 \\ 4 y\end{array}\right]$
View full solution →If $X =\left[\begin{array}{cc}4 & 1 \\ -1 & 2\end{array}\right],$ show that $6X - X^2 = 9I,$ where $I$ is unit matrix.
View full solution →If $A=\left[\begin{array}{cc}3 & 1 \\ -1 & 2\end{array}\right]$ and $B=\left[\begin{array}{l}7 \\ 0\end{array}\right]$, find matrix $C$ if $AC = B.$
View full solution →If $A=\left[\begin{array}{ll}3 & 1 \\ 2 & 1\end{array}\right]$ and $B=\left[\begin{array}{cc}1 & -2 \\ 5 & 3\end{array}\right],$ then show that $(A - B)^2 \neq A2 - 2AB + B^2.$
View full solution →If $A =\left[\begin{array}{cc}1 & 2 \\ -2 & 3\end{array}\right], B =\left[\begin{array}{ll}2 & 1 \\ 2 & 3\end{array}\right] C =\left[\begin{array}{cc}-3 & 1 \\ 2 & 0\end{array}\right]$ verify that
$A(B + C) = AB + AC$.
View full solution →If $A =\left[\begin{array}{cc}1 & 2 \\ -2 & 3\end{array}\right], B =\left[\begin{array}{ll}2 & 1 \\ 2 & 3\end{array}\right] C =\left[\begin{array}{cc}-3 & 1 \\ 2 & 0\end{array}\right]$ verify that $(AB)C = A(BC),$
View full solution →Let $A =\left[\begin{array}{ll}1 & 0 \\ 2 & 1\end{array}\right], B =\left[\begin{array}{cc}2 & 3 \\ -1 & 0\end{array}\right]$. Find $A^2 + AB + B^2$.
View full solution →Let $A =\left[\begin{array}{ll}4 & -2 \\ 6 & -3\end{array}\right], B =\left[\begin{array}{cc}0 & 2 \\ 1 & -1\end{array}\right]$ and $C =\left[\begin{array}{cc}-2 & 3 \\ 1 & -1\end{array}\right]$. Find $A^2 - A + BC$.
View full solution →If $A=\left[\begin{array}{ll}9 & 1 \\ 5 & 3\end{array}\right]$ and $B=\left[\begin{array}{cc}1 & 5 \\ 7 & -11\end{array}\right]$, find matrix $X$ such that $3A + 5B - 2X = 0.$
View full solution →