Sample QuestionsAlgebra of Matrices questions
One sample from each question group in this chapter. Select any group above to see the full set with answer keys.
If $\text{A}=\begin{bmatrix}\text{n}&0&0\\0&\text{n}&0\\0&0&\text{n}\end{bmatrix}$ and $\text{B}=\begin{bmatrix}\text{a}_1&\text{a}_2&\text{a}_3\\\text{b}_1&\text{b}_2&\text{b}_3\\\text{c}_1&\text{c}_2&\text{c}_3\end{bmatrix},$ then $AB$ is equal to:
Answer: B.
View full solution →If A is a square matrix, then AA is a:
Answer: D.
View full solution →If $\text{A}=\begin{bmatrix}2&-1&3\\-4&5&1\end{bmatrix}$ and $\text{B}=\begin{bmatrix}2&3\\4&-2\\1&5\end{bmatrix},$ then:
- A
- B
- ✓
AB and BA both are defined.
- D
AB and BA both are not defined.
Answer: C.
View full solution →If $A$ is a square matrix such that $A^2 = A,$ then $(I + A)^3 - 7A$ is equal to:
Answer: C.
View full solution →If $S = [S_{ij}]$ is a scalar matrix such that $S_{ij} = k$ and $A$ is a square matrix of the same order, then $AS = SA = ?$
Answer: C.
View full solution →If $\text{A}[\text{a}_{\text{ij}}]=\begin{bmatrix}2&3&-5\\1&4&9\\0&7&-2\end{bmatrix}$ and $\text{B}=[\text{b}_\text{ij}]=\begin{bmatrix}2&-1\\-3&4\\1&-2\end{bmatrix}$
Then find $a_{22} + b_{21}$
View full solution →Construct a $3 \times 4$ matrix $A = [a_{ij}]$ whose element $a_{ij}$ are given by:
$a_{ij} = i - j$
View full solution →In a certain city there are 30 colleges. Each college has 15 peons, 6 clerks, 1 typist and 1 section officer. Express the given information as a column matrix. Using scalar multiplication, find the total number of posts of each kind in all the colleges.
Construct a $4 \times 3$ matrix whose element are:
$a_{ij} = i$
View full solution →Construct a 4 × 3 matrix whose element are:
$\text{a}_\text{ij}=\frac{\text{i}-\text{j}}{\text{i}+\text{j}}$
View full solution →Find matrices X and Y, if $\text{X}+\text{Y}=\begin{bmatrix}5&2\\0&9\end{bmatrix}$ and $\text{X}-\text{Y}=\begin{bmatrix}3&6\\0&-1\end{bmatrix}$
View full solution →If $A = [a_{ij}]$ is a $2 \times 2$ matrix such that $a_{ij} = i + 2j$, write $A$.
View full solution →f $A$ is a matrix of order $3\times 4$ and $B$ is a matrix of order $4\times 3$, find the order of the matrix of $AB.$
View full solution →Write the number of all possible matrices of order $2\times 2$ with each entry $1, 2$ or $3.$
View full solution →If $\text{A}=\begin{bmatrix}4&3\\1&2 \end{bmatrix}$ and $\text{B}=\begin{bmatrix}-4\\3\end{bmatrix},$ write AB.
View full solution →If $\text{A}=\begin{bmatrix}\cos\alpha&\sin\alpha\\-\sin\alpha&\cos\alpha\end{bmatrix},$ then verify that $A^TA = I_2$.
View full solution →Find the matrix A such that
$\begin{bmatrix}2&-1\\1&0\\-3&4\end{bmatrix}\text{A}=\begin{bmatrix}-1&-8&-10\\1&-2&-5\\9&22&15\end{bmatrix}$
View full solution →If $\text{A}=\text{diag}\begin{pmatrix}2&-5&9\end{pmatrix},\text{ B}=\text{diag}\begin{pmatrix}1&1&-4\end{pmatrix}$ and $\text{C}=\text{diag}\begin{pmatrix}-6&3&4\end{pmatrix},$ find.
$\text{B}+\text{C}-2\text{A}$
View full solution →If $\text{A}=\begin{bmatrix}\cos\text{x}&\sin\text{x}\\-\sin\text{x}&\cos\text{x}\end{bmatrix},$ find x satisfying $0<\text{x}<\frac{\pi}{2}$ when $A + A^T = I$
View full solution →If $\text{A}=\text{diag}\begin{pmatrix}2&-5&9\end{pmatrix},\text{ B}=\text{diag}\begin{pmatrix}1&1&-4\end{pmatrix}$ and $\text{C}=\text{diag}\begin{pmatrix}-6&3&4\end{pmatrix},$ find.
$2\text{A}+3\text{B}-5\text{C}$
View full solution →Let $\text{A}=\begin{bmatrix}3 & 2&7 \\1 & 4&3\\-2&5&8 \end{bmatrix}.$ Find matrices X and Y such that X + Y = A, where X is a symmetric and Y is a skew-symmetric matrix.
View full solution →If $\text{A}=\begin{bmatrix}2&-2\\4&2\\-5&1\end{bmatrix},\text{ B}=\begin{bmatrix}8&0\\4&-2\\3&6\end{bmatrix},$ find matrix X such that 2A + 3X = 5B.
View full solution →If $\text{P}=\begin{bmatrix}\text{x}&0&0\\0&\text{y}&0\\0&0&\text{z}\end{bmatrix}$ and $\text{Q}=\begin{bmatrix}\text{a}&0&0\\0&\text{b}&0\\0&0&\text{c}\end{bmatrix},$ prove that $\text{PQ}=\begin{bmatrix}\text{xa}&0&0\\0&\text{y}\text{b}&0\\0&0&\text{zc}\end{bmatrix}=\text{QP}$
View full solution →If $\text{A}=\begin{bmatrix}2&3\\-1&0\end{bmatrix},$ show that $A^2 - 2A + 3I_2 = 0$.
View full solution →If $\text{A}=\begin{bmatrix}3&2&0\\1&4&0\\0&0&5\end{bmatrix},$ show that $A^2 - 7A + 10I_3 = 0$.
View full solution →