Question 1 :
If the matrix $\begin{bmatrix} 1 & 3 & \lambda +2 \\ 2 & 4 & 8 \\ 3 & 5 & 10 \end{bmatrix}$ is singular, then $\lambda=$
Question 2 :
What is the order of the product $ \begin{bmatrix} x & y & z \end{bmatrix} \begin{bmatrix} a & h & g \\ h & b & f \\ g & f & c \end{bmatrix} \begin{bmatrix} x \\ y \\ z \end{bmatrix}$ ?
Question 3 :
If a matrix has $m$ rows and $n$ columns then its order is
Question 4 :
A <b>matrix</b> consisting of a single <b>column</b> of m elements is know as
Question 6 :
Two matrices are equal if and only if they have the _________ and corresponding elements are _________.<br>
Question 11 :
If $A= [ 1 \ 2\ 3 ]$, then the set of elements of A is
Question 13 :
Matrix $A$ is given by $A=\begin{bmatrix} 6 & 11 \\ 2 & 4 \end{bmatrix}$ then the determinant of ${A}^{2015} -6{A}^{2014} $ is.
Question 14 :
For any square matrix $A=[{a}_{ij}],{a}_{ij}=0$, when $i\ne j$, then $A$ is
Question 15 :
Construct a $2\times3$ matrix $A = [a_{ij}]$ whose elements are given by $a_{ij} = 2(i - j)$
Question 16 :
<span>If $A=\displaystyle \left[ \begin{matrix} 1 &2 \\ 3& 4 \end{matrix} \right] $, then which of the following is not an element of $A$?</span>
Question 17 :
A $2 \times 2$ matrix whose elements $\displaystyle a_{ij}$ are given by $\displaystyle a_{ij}=i-j$ is
Question 18 :
${a}^{-1}+{b}^{-1}+{c}^{-1}=0$ such that $\begin{vmatrix} 1+a & 1 & 1 \\ 1 & 1+b & 1 \\ 1 & 1 & 1+c \end{vmatrix}=\triangle$ then the value of $\triangle$ is
Question 19 :
The number of possible orders of a matrix containing $24$ elements are:
Question 21 :
The matrix $A = \begin{bmatrix}0 & 0 &4 \\ 0 & 4 & 0\\ 4 & 0 & 0\end{bmatrix}$ is a<br>
Question 22 :
If $A=\begin{bmatrix} { a }^{ 2 } & ab & ac \\ ab & { b }^{ 2 } & bc \\ ac & bc & { c }^{ 2 } \end{bmatrix}$ and ${a}^{2}+{b}^{2}+{c}^{2}=1$ then ${A}^{2}=$
Question 24 :
If every row of a matrix $A$ contains $p$ elements and its column contains $q$ elements, then the order of $A$ is
Question 25 :
If the order of the matrix is $1\times2$, then it is a <br/>
Question 26 :
$A=\begin{bmatrix} \cos\theta & -\sin\theta \\ \sin\theta & \cos\theta\end{bmatrix}$ and $AB=BA=I$, then B is equal to
Question 27 :
If $A=\begin{bmatrix} \cos { x } & \sin { x } \\ -\sin { x } & \cos { x } \end{bmatrix}$ and $A(AdjA)=k\begin{bmatrix} 1 & 0 \\ 0 & 1 \end{bmatrix}$ then the value of $k$ is
Question 28 :
<b>If $A$ is a square of order $3$, then</b> $\left| Adj\left( Adj{ A }^{ 2 } \right)\right| =$
Question 31 :
The order of the matrix $A$ is $3\times 5$ and that of $B$ is $2\times 3$. The order of the matrix $BA$ is:
Question 32 :
$\displaystyle \begin{bmatrix}1 &0 &0 \\0 &4 &0 \\0 &0 &5 \end{bmatrix}$<span> is an:</span>
Question 33 :
If $\begin{bmatrix}4 &-3 \\ 2 & 16\end{bmatrix}$ = $\begin{bmatrix}4 &-3 \\ 2 & 2^t\end{bmatrix}$, then t = _______
Question 34 :
_____ matrix is a square matrix in which all the elements other than the principal diagonal elements are zero.<br/>
Question 35 :
$\displaystyle { A=\left[ { a }_{ ij } \right] }_{ m\times n}$ is a square matrix , if
Question 36 :
The number of different possible orders of matrices having 18 identical elements is
Question 37 :
If $A=\begin{bmatrix}5 & 2\\ 7 & 4\end{bmatrix}$ is a $2\times 2$ matrix, then $a_{12}$=
Question 38 : <div>If $\begin{bmatrix}r+4 & 6 \\3 & 3\end{bmatrix} = \begin{bmatrix} 5 & r+5 \\ r+2 & 4 \end{bmatrix}$ then $r= $ </div><div><br/></div>
Question 39 :
If a matrix has equal number of columns and rows then it is said to be a
Question 42 :
Construct the matrix of order $3 \times 2$ whose elements are given by $a_{ij} = 2i - j$
Question 43 :
The number of all possible matrices of order $3 \times 3$ with each entry $0$ or $1$ is:
Question 44 :
A matrix having $m$ rows and $n$ columns with $m=n$ is said to be a
Question 45 :
Let $A$ be a matrix such that $A \cdot \left[ \begin{array} { c c } { 1 } & { 2 } \\ { 0 } & { 3 } \end{array} \right]$ is a scalar matrix and $| 3 A | = 108 .$ Then <span> $A \cdot \left[ \begin{array} { c c } { 1 } & { 2 } \\ { 0 } & { 3 } \end{array} \right]$is equal to</span>
Question 46 :
If a matrix has $13$ elements, then the possible<br>dimensions (orders) of the matrix are
Question 47 :
If $A$ is square matrix such that ${A^2} = 1$ then ${A^{ - 1}} = ?$
Question 48 :
$A=\begin{bmatrix} a & b \\ 0 & c \end{bmatrix}$ then ${A}^{-1}+(A-aI)(A-cI)=$
Question 49 :
If $A = {\left( {{a_{ij}}} \right)_{2 \times 2}}$, where ${a_{ij}} = i + j$, then $A$ is equal to:<br/>
Question 50 :
Possible number of labelled simple Directed, Pseudo and Multigarphs exist having 2 vertices are<span><br/></span>
Question 51 :
If a matrix is of order $2 \times 3$, then the number of elements in the matrix is<br>
Question 52 :
For a matrix $A \begin{pmatrix} 1& 0 & 0\\ 2 & 1 & 0\\ 3 & 2 & 1\end{pmatrix}$, if $U_{1}, U_{2}$ and $U_{3}$ are $3\times 1$ column matrices satisfying $AU_{1} = \begin{pmatrix}1\\ 0 \\ 0<br>\end{pmatrix}, AU_{2} \begin{pmatrix}2\\3 \\ 0<br>\end{pmatrix}, AU_{3} = \begin{pmatrix}2\\ 3\\ 1<br>\end{pmatrix}$ and $U$ is $3\times 3$ matrix whose columns are $U_{1}, U_{2}$ and $U_{3}$<br>Then sum of the elements of $U^{-1}$ is<br>
Question 53 :
Assertion: If $A = \begin{bmatrix} \cos \alpha & \sin \alpha \\ \cos \alpha & \sin \alpha\end{bmatrix}$ and $B = \begin{bmatrix} \cos \alpha & \cos \alpha \\ \sin \alpha & \sin \alpha\end{bmatrix}$, then $AB = \begin{bmatrix} 1 & 1 \\<br/>1 & 1 \end{bmatrix}$.
Reason: The product of two matrices can never be equal to an unit matrix.
Question 55 :
If $A=\begin{vmatrix} \begin{matrix} -2 \\ 4 \end{matrix} \\ 5 \end{vmatrix},\,B=\begin{vmatrix} \begin{matrix} 1 & 3 & -6 \end{matrix} \end{vmatrix}$, State whether ist is true or false ${(AB)}^{1}={B}^{1}\,{A}^{1}$
Question 56 :
If the order of a matrix is $\displaystyle 20\times 5$ then the number of elements in the matrix is _____
Question 57 :
If $A=\begin{bmatrix} 2 &-3 \\ -4&-1 \end{bmatrix}$, then adj $(3A^{2}+12A)$ is equal to:
Question 58 :
If $\left[\begin{array}{ll}<br/>r+2 & 5\\<br/>-2 & r+1<br/>\end{array}\right]=\left[\begin{array}{lll}<br/>4 & y+3\\<br/>z & 3<br/>\end{array}\right]$, then<br/>
Question 59 :
If $\left[\begin{array}{ll}<br/>x+3 & 2y+x\\<br/>z-1 & 4a-z<br/>\end{array}\right]=\left[\begin{array}{ll}<br/>0 & -7\\<br/>3 & 2a<br/>\end{array}\right],$ then $(x+y+z+a)$ is:
Question 60 :
Obtain the inverse of the following matrix using elementary operation:<br/>$A = \begin{bmatrix} 3 & 0 & -1 \\ 2 & 3 & 0 \\ 0 & 4 & 1 \end{bmatrix}$<br/>
Question 61 :
Let $A+2B\ =\ \left[ \begin{matrix} 1 & 2 & 0 \\ 6 & -3 & 3 \\ -5 & 3 & 1 \end{matrix} \right] $ and $2A-B= \left[ \begin{matrix} 2 & -1 & 5 \\ 2 & -1 & 6 \\ 0 & 1 & 2 \end{matrix} \right] $ then Det ($Tr(A)-Tr(B)$) has the value equal to
Question 62 :
If A is $3 \times 4$ matrix and B is matrix such that A'B and BA' are both defined, then B is of the type.<br>
Question 63 :
Assertion: The possible dimension of a matrix consisting $27$ elements is $4.$
Reason: The number of ways of expressing $27$ as a product of two positive integers is $4.$
Question 64 :
If matrix $AB=0$, then $A=0$ or $B=0$ or both $A$ and $B$ null matrices.
Question 65 :
The value of $x$, for which the matrix $A = \begin{bmatrix}e^{x - 2} & e^{7 + x}\\ e^{2 + x} & e^{2x + 3}\end{bmatrix}$ is singular, is<br>
Question 66 :
The order of any matrix is $3\times 2$ then no. of element in the matrix?
Question 67 :
Inverse of <span>$A = \begin{bmatrix} 1& 3\\ 2 & -2\end{bmatrix} $ is equal to?</span><span><span class="MathJax"></span><span class="MathJax"><span class="MJX_Assistive_MathML">A </span></span></span>
Question 68 :
If $A$ is a square matrix such that $A^{2} = I$, then $(A - I)^{3} + (A + I)^{3} - 7A$ is equal to
Question 69 :
$\begin{vmatrix} x+5 & x \\ x+9 & x-2 \end{vmatrix}=0$ then x=
Question 70 :
If $A$ and $B$ are non - zero square matrices of the same order such that $AB = 0$, then
Question 71 :
If $A$ and $B$ are matrices of order $3\times 2$ and $C$ is of order $2\times 3$, then which of the following matrices is not defined-
Question 72 :
Let $\begin{bmatrix} 1 & 1\\ 0 & 1\end{bmatrix} \begin{bmatrix} 1 & 2\\ 0 & 1\end{bmatrix} \begin{bmatrix} 1 & 3\\ 0 & 1\end{bmatrix}.\begin{bmatrix} 1 & n-1\\ 0 & 1\end{bmatrix}=\begin{bmatrix} 1 & 78\\ 0 & 1\end{bmatrix}$<br>If $A=\begin{bmatrix} 1 & n\\ 0 & 1\end{bmatrix}$ then $A^{-1}=?$<br>
Question 73 :
Assertion: The matrix $\begin{bmatrix} a & 0 & 0 & 0 \\ 0 & b & 0 & 0 \\ 0 & 0 & c & 0 \end{bmatrix}$ is a diagonal matrix
Reason: $A[{a}_{ij}]$ is a square matrix such that ${a}_{ij}=0$ for all $i\ne j$, then $A$ is called diagonal matrix
Question 75 :
Inverse of the matrix $\begin{bmatrix} \cos 2\theta & -\sin 2\theta\\ \sin 2\theta & \cos 2\theta\end{bmatrix}$ is.
Question 76 :
Number of real values of $\begin{vmatrix} 3-x & 2 & 2 \\ 2 & 4-x & 1 \\ -2 & -4 & -1-x \end{vmatrix}$ is singular, then
Question 77 :
If A is a square matrix of order n, then adj (adj A ) is equal to
Question 80 :
The matrix $P=\begin{bmatrix} 0 & 0 & 4 \\ 0 & 4 & 0 \\ 4 & 0 & 0 \end{bmatrix}$ is a
Question 81 :
If $\bigl(\begin{smallmatrix} 3x+ 7& 5 \\ y + 1 & 2 - 3x\end{smallmatrix}\bigr) = \bigl(\begin{smallmatrix}1 & y - 2 \\ 8 & 8\end{smallmatrix}\bigr)$ then the values of x and y respectively are<br>
Question 82 :
If $\triangle =\left| \begin{matrix} arg{ z }_{ 1 } & arg{ z }_{ 2 } & arg{ z }_{ 3 } \\ arg{ z }_{ 2 } & arg{ z }_{ 3 } & arg{ z }_{ 1 } \\ arg{ z }_{ 3 } & arg{ z }_{ 1 } & arg{ z }_{ 2 } \end{matrix} \right| $, the, $\triangle$ is divided by:
Question 83 :
If $A$ is matrix or order $m\times n$ and $B$ is a matrix such that $AB'$ and $B'A$ are both defined, then order of matrix $B$ is
Question 84 :
If the square of the matrix $\begin{bmatrix} a & b \\ a & -a \end{bmatrix}$ is the unit matrix, then $b$ is equal to
Question 85 :
If the order of matrices $A$ and $B$ are $3 \times 2$ and $2 \times 1 $ respectively, then find the order of matrix (if possible) $AB$
Question 87 :
The matrix $A=\begin{bmatrix} 0 & 0 & 5 \\ 0 & 5 & 0 \\ 5 & 0 & 0 \end{bmatrix}$ is a
Question 88 :
Given the equality of the following determinants. Find the value of $(a+b)$.<br>$\begin{vmatrix} 4 & 3\\ 6 & a\end{vmatrix} = \begin{vmatrix} 6 & b \\ 4 & 5\end{vmatrix}$<br><br>
Question 89 :
Let $A$ is a square matrix of order $n$ and $a$ being a scalar then $|aA|=$
Question 91 :
$A=\begin{bmatrix} 1 & 2 & 3 \\ 1 & 2 & 3 \\ -1 & -2 & -3 \end{bmatrix}$, then A is a nilpotent matrix of index
Question 92 :
If $\displaystyle a_{ij}=0\left ( i\neq j \right )$ and $\displaystyle a_{ij}=1\left ( i= j \right )$ then the matrix A= $\displaystyle \left [ a_{ij} \right ]_{n\times n}$ is a _____ matrix
Question 93 :
If $\begin{bmatrix} 1 & 2 \\ 3 & -5 \end{bmatrix}$, then ${A}^{-1}$ is equal to
Question 94 :
The equation, $\left[ \begin{matrix} 1 & x & y \end{matrix} \right] \left[ \begin{matrix} 1 & 3 & 1 \\ 0 & 2 & -1 \\ 0 & 0 & 1 \end{matrix} \right] \left[ \begin{matrix} 1 \\ x \\ y \end{matrix} \right] =\left[ 0 \right] $ has for<br/>(i) $y=0$, (p) rational roots<br/>(ii) $y=-1$ (q) irrational roots<br/> (r) integral roots<br/>
Question 95 :
Assertion: The matrix $\displaystyle \begin{pmatrix}.<br/><br/>1 &0 &0 &0 \\0 &2 &0 &0 \\0 &0 &3 &0 \end{pmatrix} $ is a diagonal matrix
Reason: $\displaystyle A=(a_{ij})_{m\times m}$ is a square matrix such that entry $\displaystyle a_{ij}=0\forall i\neq j,$ then A is called diagonal matrix.
Question 96 :
If $A = \begin{bmatrix}1 & 3 & 1\\ 2 & 1 & -1\\ 3 & 0 & 1\end{bmatrix}$, then rank $(A)$ is equal to<br>
Question 97 :
A is an involutory matrix given by $A=\begin{bmatrix} 0 & 1 & -1 \\ 4 & -3 & 4 \\ 3 & -3 & 4 \end{bmatrix}$ then the inverse of $\dfrac{A}{2}$ will be
Question 98 : <table class="wysiwyg-table"><tbody><tr><td></td><td>Day 1</td><td>Day 2</td><td>Day 3</td></tr><tr><td>Model X</td><td>$20$</td><td>$18$</td><td>$3$</td></tr><tr><td>Model Y</td><td>$16$</td><td>$5$</td><td>$8$</td></tr><tr><td>Model Z</td><td>$19$</td><td>$11$</td><td>$10$</td></tr></tbody></table>The table above shows the number of TV sets that were sold during a three-day sale. The prices of models $X, Y$ and $Z$ are $ $99$, $ $199$, and $ $299$, respectively. Which of the following matrix representations gives the total income, in dollars, received from the sale of the TV sets for each of the three days?
Question 99 :
If $A$ is a square matrix of order $3$ such that $A^{2} + A + 4I = 0$, where $0$ is the zero matrix and $I$ is the unit matrix of order $3$, then
Question 100 : <div><span>$B=A+A^{2}+A^{3}+A^{4}$ </span><br/></div><div><span>If order of $A$ is $3$ then order of $B$ is </span></div>
Question 101 :
If $\begin{vmatrix} x-4 & 2x & 2x \\ 2x & x-4 & 2x \\ 2x & 2x & x-4 \end{vmatrix}$ = $(A+Bx)(x-A)^2$,<br>then the ordered pair $(A , B)$ is equal to:
Question 102 : <div>If $0\le\left[x\right]<2,\,-1\le\left[y\right]<1$ and $1\le\left[z\right]<3$ ( $\left[.\right]$ denotes the greatest integer function) then the maximum value of determinant</div><div>$\Delta=\left| \begin{matrix} \left[x\right]+1 & \left[y\right] & \left[z\right] \\ \left[x\right] & \left[y\right]+1 & \left[z\right] \\ \left[x\right] & \left[y\right] & \left[z\right]+1 \end{matrix} \right|$ is</div>
Question 103 : Let $n\ge 2$ be an integer,<div><br/>$A=\begin{bmatrix} \cos { \left( { \dfrac{2\pi}n} \right) } & \sin { \left(\dfrac{2\pi}n \right) } & 0 \\ -\sin { \left( \dfrac{2\pi}n \right) } & \cos { \left(\dfrac{2\pi}n \right) } & 0 \\ 0 & 0 & 1 \end{bmatrix}$ and $I$ is the identity matrix of order $3$., then following of which is correct</div>
Question 104 :
If $A$ is $2\times 3$ matrix and $AB$ is a $2\times 5$ matrix, then $B$ must be a
Question 105 :
If the matrix $\begin{bmatrix} 0 & 2\beta & \Upsilon \\ \alpha & \beta & -\Upsilon \\ \alpha & -\beta & \Upsilon \end{bmatrix}$is orthogonal, then
Question 106 :
If $A(\theta )=\begin{bmatrix} \cos \theta & -\sin \theta &0 \\\sin \theta &\cos \theta &0 \\0 &0 &0 \end{bmatrix}$, then $A(\theta )^3$ will be a null matrix if and only if<br>
Question 107 :
What is the inverse of the matrix<br/>$A=\begin{bmatrix} \cos { \theta } & \sin { \theta } & 0 \\ -\sin { \theta } & \cos { \theta } & 0 \\ 0 & 0 & 1 \end{bmatrix}$ ?
Question 108 :
Consider $A$ and $B$ two square matrices of same order. Select the correct alternative.
Question 109 :
$\left[ \begin{matrix} x \\ 3 \end{matrix}\begin{matrix} 6 \\ 2x \end{matrix} \right]$ is a singular matrix, then $x$ is equal to
Question 110 :
When a row matrix is multiplied by a column matrix both having the same number of elements, the resulting matrix formed is a ___?
Question 111 :
$\displaystyle \begin{vmatrix} 1 & a & {a}^{2}-bc \\ 1 & b & {b}^{2}-ca \\ 1 & c & {c}^{2}-ab \end{vmatrix}$=?
Question 112 :
Assertion: If $D = diag [d_1, d_2, ...., d_n]$, then $D^{-1} = diag [d_1^{-1}, d_2^{-1} ..... , d_n^{-1}]$
Reason: If $D = diag [d_1, d_2, ...... d_n], $ then $D^n = diag [d_1^n, d_2^n ...... , d_n^n].$
Question 113 :
Two rectangular matrices of order $n\times m$ and $m\times k$ are multiplied in the same order. The resulting matrix formed is a:
Question 114 :
If D$_1$ and D$_2$ are two 3 $\times$ 3 diagonal matrices, then which of the following is/are true?
Question 115 :
If the number of elements in a matrix is $60$ then how many different order of matrix are possible
Question 116 :
Out of the following matrices, choose that matrix which is a scalar matrix.
