Sample QuestionsMatrices questions
One sample from each question group in this chapter. Select any group above to see the full set with answer keys.
Classify the following matrix :
$
\left|\begin{array}{lll}
11 & 3 & 0 \\
21 & 8 & 4 \\
15 & 5 & 2
\end{array}\right|
$
View full solution →Classify the following matrix $: \left|\begin{array}{ll} 1 & 1 \\ 0 & 9 \end{array}\right| $
View full solution →Classify the following matrix $: \left|\begin{array}{l} 800 \\ 521 \end{array}\right| $
View full solution →Classify the following matrix : $\left[7 0\right]$
View full solution →If $P = (8 , 5),(7 , 2),$ find $P^t$
View full solution →If $A=\left|\begin{array}{ll}1 & 3 \\ 3 & 2\end{array}\right|$ and $B=\left|\begin{array}{ll}-2 & 3 \\ -4 & 1\end{array}\right|$ find $B A$
View full solution →If $A=\left|\begin{array}{ll}1 & 3 \\ 3 & 2\end{array}\right|$ and $B=\left|\begin{array}{ll}-2 & 3 \\ -4 & 1\end{array}\right|$ find $A B$
View full solution →Evaluate the following:
$
\left|\begin{array}{ccc}
0 & 1 & 0 \\
2 & 0 & -3 \\
1 & 0 & -2
\end{array}\right|\left|\begin{array}{cc}
1 & -2 \\
3 & 4 \\
0 & 0
\end{array}\right|
$
View full solution →Evaluate the following:
$
\left|\begin{array}{ll}
6 & 1 \\
3 & 1 \\
2 & 4
\end{array}\right|\left|\begin{array}{ccc}
1 & -2 & 1 \\
2 & 1 & 3
\end{array}\right|
$
View full solution →Evaluate the following $: \left|\begin{array}{cc} 0 & 1 \\ -1 & 2 \\ -2 & 0 \end{array}\right|\left|\begin{array}{ccc} 0 & -4 & 0 \\ 3 & 0 & -1 \end{array}\right| $
View full solution →Let $A$ be a $2 \times 2$ matrix and let $I$ be an identity matrix of the order $2 \times 2.$ Prove that $AI = IA = A.$
View full solution →Evaluate the following $: \left|\begin{array}{ll} \mid 3 & 2 \end{array}\right|\left|\begin{array}{c} -1 \\ 3 \end{array}\right| $
View full solution →If $A =\left|\begin{array}{l}1215 \\ 1117\end{array}\right|$ and $B =\left|\begin{array}{ll}2 & 7 \\ 4 & 9\end{array}\right|$ find $:2 A +3 B$
View full solution →Find the values of $x$ and $y$, if $\left|\begin{array}{c}3 x-y \\ 5\end{array}\right|=\left|\begin{array}{c}7 \\ x+y\end{array}\right|$
View full solution →Find the values of a and b) if [2a + 3b a - b] = [19 2].
Let $A=\left|\begin{array}{ll}3 & 2 \\ 0 & 5\end{array}\right|$ and $B=\left|\begin{array}{ll}1 & 0 \\ 1 & 2\end{array}\right|$, find $(i) \ (A+B)(A-B) \ (ii) \ A^2-B^2$. Is $(i)$ equal to $(ii)$ ?
View full solution →If $A =\left|\begin{array}{cc}3 & -2 \\ -1 & 4\end{array}\right|, B =\left|\begin{array}{c}2 a \\ 1\end{array}\right|, C =\left|\begin{array}{c}-4 \\ 5\end{array}\right|, D =\left|\begin{array}{l}2 \\ b \end{array}\right|$ and $AB +2 C =4 D$ then find the values of $a$ and $b$.
View full solution →If $X=\left|\begin{array}{cc}1 & -2 \\ 1 & 3\end{array}\right|, Y=\left|\begin{array}{cc}-3 & 0 \\ 4 & 1\end{array}\right|$ and $Z=\left|\begin{array}{cc}5 & -1 \\ 3 & 2\end{array}\right|$, prove that $X(Y+Z)=X Y+X Z$
View full solution →If $\left|\begin{array}{ll}3 a +2 b & 2 a - b \\ 4 p -3 q & 2 p + q \end{array}\right|=\left|\begin{array}{cc}12 & 1 \\ 16 & 8\end{array}\right|$, find the values of $a , b , p$ and $q.$
View full solution →If $A =\left|\begin{array}{cc} p & q \\ 8 & 5\end{array}\right|, B =\left|\begin{array}{cc}3 p & 5 q \\ 2 q & 7\end{array}\right|$ and if $A + B =\left|\begin{array}{cc}12 & 6 \\ 2 r & 3 s \end{array}\right|$, find the values of $p , q , r$ and $s$.
View full solution →Find $X$ and $Y,$ if $\left|\begin{array}{cc}1 & 2 \\ 2 & -3\end{array}\right|\left|\begin{array}{l}x \\ y\end{array}\right|=\left|\begin{array}{c}-1 \\ 12\end{array}\right|$
View full solution →If $P=\left|\begin{array}{ll}1 & 2 \\ 3 & 4\end{array}\right|, Q=\left|\begin{array}{ll}5 & 1 \\ 7 & 4\end{array}\right|$ and $R=\left|\begin{array}{ll}2 & 1 \\ 4 & 2\end{array}\right|$ find the value of $(R+Q) P$
View full solution →If $P=\left|\begin{array}{ll}1 & 2 \\ 3 & 4\end{array}\right|, Q=\left|\begin{array}{ll}5 & 1 \\ 7 & 4\end{array}\right|$ and $R=\left|\begin{array}{ll}2 & 1 \\ 4 & 2\end{array}\right|$ find the value of $P(Q+R)$
View full solution →If $P=\left|\begin{array}{ll}1 & 2 \\ 2 & 1\end{array}\right|$ and $Q=\left|\begin{array}{ll}2 & 1 \\ 1 & 2\end{array}\right|$ find $P(Q P)$.
View full solution →Find the values of $a , b , c$ and $d$, if $\left|\begin{array}{ll} a +3 b & 3 c + d \\ 2 a - b & c -2 d \end{array}\right|=\left|\begin{array}{ll}5 & 8 \\ 3 & 5\end{array}\right|$
View full solution →