MCQ 11 Mark
Directions: In the following questions, a statement of assertion $(A)$ is followed by a statement of reason $(R).$ Mark the correct choice as:
Assertion: Let $\text{A}_{\theta}=\begin{pmatrix}\cos\theta+\sin\theta&\sqrt{2}\sin\theta\\-\sqrt{2}\sin\theta&\cos\theta-\sin\theta\end{pmatrix}\Big(\text{A}_{\frac{\pi}{3}}\Big)^{3}=-\text{I}.$
Reason: $\text{A}_{\theta}\cdot\text{A}_{\phi}=\text{A}_{\theta+\phi}.$
- ✓
Both $A$ and $R$ are true and $R$ is the correct explanation of $A.$
- B
Both $A$ and $R$ are true but $R$ is not the correct explanation of $A.$
- C
$A$ is true but $R$ is false.
- D
$A$ is false but $R$ is true.
AnswerCorrect option: A. Both $A$ and $R$ are true and $R$ is the correct explanation of $A.$
View full question & answer→MCQ 21 Mark
Directions: In the following questions, a statement of assertion $(A)$ is followed by a statement of reason $(R)$. Mark the correct choice as:
Assertion: If $\text{A}=\begin{pmatrix}0 & 2 & -1\\ -2 & 0 & 3 \\ 1& -3 & 0 \end{pmatrix},$ then $A^{-1}$ is symmetric matrix.
Reason: If $A$ is skew symmetric matrix then $A^{-1}$ is skew symmetric matrix.
- ✓
Both $A$ and $R$ are true and $R$ is the correct explanation of $A$.
- B
Both $A$ and $R$ are true but $R$ is not the correct explanation of $A.$
- C
$A$ is true but $R$ is false.
- D
$A$ is false but $R$ is true.
AnswerCorrect option: A. Both $A$ and $R$ are true and $R$ is the correct explanation of $A$.
View full question & answer→MCQ 31 Mark
Directions: In the following questions, a statement of assertion $(A)$ is followed by a statement of reason $(R).$ Mark the correct choice as:
Assertion: If $A$ is a square matrix such that $A^2 = I, $ then $(I + A)^2 - 3A = I.$
Reason: $Al = IA = A,$ where $I$ is Idetity matrix.
- A
Both $A$ and $R$ are true and $R$ is the correct explanation of $A.$
- B
Both $A$ and $R$ are true but $R$ is not the correct explanation of $A.$
- C
$A$ is true but $R$ is false.
- ✓
$A$ is false but $R$ is true.
AnswerCorrect option: D. $A$ is false but $R$ is true.
View full question & answer→MCQ 41 Mark
Directions: In the following questions, a statement of assertion $(A)$ is followed by a statement of reason $(R).$ Mark the correct choice as:
Assertion: If $\text{A}=\begin{pmatrix}3&-2&10\\-2&4&5\\10&5&6\end{pmatrix}$ and $\text{x}=\begin{pmatrix}1&5&6\\-2&0&1\\4&3&2\end{pmatrix} X\ 'AX$ is symmetric matrix.
Reason: $X\ 'AX$ is symmetric or skew symmetric as $A$ is symmetric or skew symmetric.
- ✓
Both $A$ and $R$ are true and $R$ is the correct explanation of $A.$
- B
Both $A$ and $R$ are true but $R$ is not the correct explanation of $A.$
- C
$A$ is true but $R$ is false.
- D
$A$ is false but $R$ is true.
AnswerCorrect option: A. Both $A$ and $R$ are true and $R$ is the correct explanation of $A.$
View full question & answer→MCQ 51 Mark
Directions: In the following questions, a statement of assertion $(A)$ is followed by a statement of reason $(R)$. Mark the correct choice as:
Assertion: If $\text{A}=\begin{pmatrix}1 & 2 & -1\\ 2 & 0 & 3 \\ -1& 3 & 4 \end{pmatrix},$ then $A^{-1}$ is symmetric matrix.
Reason: If $A$ is symmetric matrix then $A^{-1}$ is symmetric matrix.
- ✓
Both $A$ and $R$ are true and $R$ is the correct explanation of $A.$
- B
Both $A$ and $R$ are true but $R$ is not the correct explanation of $A.$
- C
$A$ is true but $R$ is false.
- D
$A$ is false but $R$ is true.
AnswerCorrect option: A. Both $A$ and $R$ are true and $R$ is the correct explanation of $A.$
View full question & answer→MCQ 61 Mark
Directions: In the following questions, a statement of assertion $(A)$ is followed by a statement of reason $(R).$ Mark the correct choice as:
Assertion: $(\text{A}+\text{B})^{2}\neq\text{A}^{2}+2\text{AB}+\text{B}^{2}.$
Reason: Generally $AB = BA.$
- A
Both $A$ and $R$ are true and $R$ is the correct explanation of $A.$
- B
Both $A$ and $R$ are true but $R$ is not the correct explanation of $A.$
- ✓
$A$ is true but $R$ is false.
- D
$A$ is false but $R$ is true.
AnswerCorrect option: C. $A$ is true but $R$ is false.
View full question & answer→MCQ 71 Mark
Directions: In the following questions, a statement of assertion $(A)$ is followed by a statement of reason $(R)$. Mark the correct choice as:
Assertion: If $\text{A}=\begin{pmatrix}-3 & 2 \\ -5 & 4 \end{pmatrix}$ and $\text{B}=\begin{pmatrix}4&-2\\5&-3\end{pmatrix}.$ then $A^{100}B = BA^{100}.$
Reason: If $AB = BA$
$\Rightarrow A^nB = BA^n$ for all positive integers $n.$
- ✓
Both $A$ and $R$ are true and $R$ is the correct explanation of $A$.
- B
Both $A$ and $R$ are true but $R$ is not the correct explanation of $A.$
- C
$A$ is true but $R$ is false.
- D
$A$ is false but $R$ is true.
AnswerCorrect option: A. Both $A$ and $R$ are true and $R$ is the correct explanation of $A$.
View full question & answer→MCQ 81 Mark
Directions: In the following questions, a statement of assertion $(A)$ is followed by a statement of reason $(R).$ Mark the correct choice as:
Assertion: If the matrix $\text{P}=\begin{pmatrix}0&2\text{b}&-2\\3&1&3\\3\text{a}&3&3\end{pmatrix}$ is a symmetric matrix, then $\text{a}=-\frac{2}{3}$ and $\text{b}=-\frac{2}{3}.$
Reason: If $P$ is a symmetric matrix, then $P\ ' = P.$
- ✓
Both $A$ and $R$ are true and $R$ is the correct explanation of $A.$
- B
Both $A$ and $R$ are true but $R$ is not the correct explanation of $A.$
- C
$A$ is true but $R$ is false.
- D
$A$ is false but $R$ is true.
AnswerCorrect option: A. Both $A$ and $R$ are true and $R$ is the correct explanation of $A.$
View full question & answer→MCQ 91 Mark
Directions: In the following questions, a statement of assertion $(A)$ is followed by a statement of reason $(R)$. Mark the correct choice as:
Assertion: If $\text{A}=\begin{pmatrix}1&\pi\\0&1\end{pmatrix},$ then $\text{A}^{100}=\begin{pmatrix}1&100\pi\\0&1\end{pmatrix}.$
Reason: If $B$ is matrix of order 2X2 and $B^2 = O$, then $(I + B)^n = I + nB$, for all $\text{n}\in\text{N}.$
- ✓
Both $A$ and $R$ are true and $R$ is the correct explanation of $A.$
- B
Both $A$ and $R$ are true but $R$ is not the correct explanation of $A.$
- C
$A$ is true but $R$ is false.
- D
$A$ is false but $R$ is true.
AnswerCorrect option: A. Both $A$ and $R$ are true and $R$ is the correct explanation of $A.$
Both $A$ and $R$ are true and $R$ is the correct explanation of $A$.
View full question & answer→MCQ 101 Mark
Directions : In the following questions, a statement of assertion $(A)$ is followed by a statement of reason $(R).$ Mark the correct choice as:
Assertion : If $\text{A}=\begin{pmatrix}0&-2&3\\ 2&0&6\\-3&-6&0 \end{pmatrix},$ then $A^{-1}$ does not exist.
Reason : If $A$ is a skew symmetric matrix of odd order, then $A$ is singular.
- ✓
Both $A$ and $R$ are true and $R$ is the correct explanation of $A.$
- B
Both $A$ and $R$ are true but $R$ is not the correct explanation of $A.$
- C
$A$ is true but $R$ is false.
- D
$A$ is false but $R$ is true.
AnswerCorrect option: A. Both $A$ and $R$ are true and $R$ is the correct explanation of $A.$
Both $A$ and $R$ are true and $R$ is the correct explanation of $A.$
View full question & answer→MCQ 111 Mark
Directions: In the following questions, a statement of assertion $(A)$ is followed by a statement of reason $(R)$. Mark the correct choice as:
Assertion: Matrix $\text{A}=\begin{pmatrix}1 & 2 \\ -2 & 1\end{pmatrix},$ satisfies the equation $x_2 - 2x + 5I = 0,$ then $A$ is invertible.
Reason: If a square matrix satisfies the equation $a_nX^n + a_{n-1}X^{n-1} + .... + a_1X + a_nI^z = 0$ and $\text{a}_\text{n}\neq0,$ Then $A$ is invertible.
- ✓
Both $A$ and $R$ are true and $R$ is the correct explanation of $A.$
- B
Both $A$ and $R$ are true but $R$ is not the correct explanation of $A$.
- C
$A$ is true but $R$ is false.
- D
$A $ is false but $R$ is true.
AnswerCorrect option: A. Both $A$ and $R$ are true and $R$ is the correct explanation of $A.$
View full question & answer→MCQ 121 Mark
Directions: In the following questions, a statement of assertion $(A)$ is followed by a statement of reason $(R)$. Mark the correct choice as:
Assertion: If $\text{A}=\begin{pmatrix}1 & 2\\ 2& 3 \end{pmatrix}$ and $\text{B}=\begin{pmatrix}-1&4\\0&5\end{pmatrix}.$ $(A + B)^2 = A^2 + 2AB + B^2.$
Reason: $\text{AB}\neq\text{BA}.$
- A
Both $A$ and $R$ are true and $R$ is the correct explanation of $A.$
- B
Both $A$ and $R$ are true but $R$ is not the correct explanation of $A.$
- C
$A$ is true but $R$ is false.
- ✓
$A$ is false but $R$ is true.
AnswerCorrect option: D. $A$ is false but $R$ is true.
View full question & answer→MCQ 131 Mark
Directions: In the following questions, a statement of assertion $(A)$ is followed by a statement of reason $(R).$ Mark the correct choice as:
Assertion: Suppose $\text{X}=\begin{pmatrix}\text{a}&\text{b}\\\text{c}&\text{d}\end{pmatrix}$ satisfies $X2 - 4X + 3I = O.$ : If $\text{a}+\text{d}\neq4,$ then there are just two matrices such $X.$
Reason: There are infinitely many matrices $X$ satisfies the equation $X2 - 4X + 3I = O.$
- A
Both $A$ and $R$ are true and $R$ is the correct explanation of $A.$
- ✓
Both $A$ and $R$ are true but $R$ is not the correct explanation of $A.$
- C
$A$ is true but $R$ is false.
- D
$A$ is false but $R$ is true.
AnswerCorrect option: B. Both $A$ and $R$ are true but $R$ is not the correct explanation of $A.$
View full question & answer→MCQ 141 Mark
Directions: In the following questions, a statement of assertion $(A)$ is followed by a statement of reason $(R).$ Mark the correct choice as:
Assertion: Let $A$ and $B$ are $2 \times 2$ matrices. $AB = I_2$
$\Rightarrow A = B^{-1}.$
Reason:$ AB = 0$
$\Rightarrow A = 0$ or $B = 0.$
- A
Both $A$ and $R$ are true and $R$ is the correct explanation of $A.$
- B
Both $A$ and $R$ are true but $R$ is not the correct explanation of $A.$
- ✓
$A$ is true but $R$ is false.
- D
$A$ is false but $R$ is true.
AnswerCorrect option: C. $A$ is true but $R$ is false.
View full question & answer→MCQ 151 Mark
Directions: In the following questions, a statement of assertion $(A)$ is followed by a statement of reason $(R).$ Mark the correct choice as:
Assertion: Let $\text{A}=\begin{pmatrix}\text{a}&\text{b}\\\text{c}&\text{d}\end{pmatrix}$ and $\text{X}=\begin{pmatrix}\text{x}\\\text{y}\end{pmatrix}.$ If $X\ 'AX = O$ for each $X,$ then $A$ must be skew symmetric matrix.
Reason: If $A$ is symmetric matrix and $X\ 'AX = O$ for each $X,$ then $A = O.$
- A
Both $A$ and $R$ are true and $R$ is the correct explanation of $A.$
- ✓
Both $A$ and $R$ are true but $R$ is not the correct explanation of $A.$
- C
$A$ is true but $R$ is false.
- D
$A$ is false but $R$ is true.
AnswerCorrect option: B. Both $A$ and $R$ are true but $R$ is not the correct explanation of $A.$
View full question & answer→MCQ 161 Mark
Assertion (A): For any symmetric matrix A, B'AB is a skew-symmetric matrix.
Reason (R): A square matrix P is skew-symmetric if P'$P^{\prime}=-P$.
- A
Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of the Assertion (A).
- B
Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct explanation of the Assertion (A).
- C
Assertion (A) is true, but Reason (R) is false.
- D
Assertion (A) is false, but Reason (R) is true.
Answer$\because A$ is symmetric matrix
$\Rightarrow A^{\prime}=A$ ......(i)
Now, $\left(B^{\prime} A B\right)^{\prime}=B^{\prime} A^{\prime}\left(B^{\prime}\right)^{\prime}=B^{\prime} A B$ (using (i)) $\Rightarrow B^{\prime} A B$ is a symmetric matrix
So, assertion is false but reason is true.
View full question & answer→MCQ 171 Mark
Assertion $(A)$ : If $\left[\begin{array}{ll}x & 1\end{array}\right]\left[\begin{array}{cc}1 & 0 \\ -2 & 3\end{array}\right]\left[\begin{array}{c}x \\ -5\end{array}\right]=0$, then value of $x$ is either $-3 $ or $ 5 $.
Reason $(R)$ : Two matrices $\left(\begin{array}{ll}x & y \\ u & v\end{array}\right)$ and $\left(\begin{array}{ll}a & b \\ c & d\end{array}\right)$ are equal if and only if their corresponding entries are equal.
- ✓
Both $(A)$ and $(R)$ are true and $(R)$ is the correct explanation of $(A)$.
- B
Both $(A)$ and $(R)$ are true but $(R)$ is not the correct explanation of $(A)$.
- C
$(A)$ is true but $(R)$ is false.
- D
$(A)$ is false but $(R)$ is true.
AnswerCorrect option: A. Both $(A)$ and $(R)$ are true and $(R)$ is the correct explanation of $(A)$.
Given $\left[\begin{array}{ll}x & 1\end{array}\right]\left[\begin{array}{cc}1 & 0 \\ -2 & 3\end{array}\right]\left[\begin{array}{c}x \\ -5\end{array}\right]=0$
$\Rightarrow [(x-2) 3]\left[\begin{array}{c} x \\ -5 \end{array}\right]=O $
$\Rightarrow x(x-2)-15=0$
$ \Rightarrow x^2-2 x-15=0 $
$\Rightarrow x=-3,5$
$\therefore$ Assertion and Reason both are true and Reason is the correct explanation of Assertion.
View full question & answer→MCQ 181 Mark
Assertion (A): The matrix $A=\left(\begin{array}{ccc}0 & a & b \\ -a & 0 & c \\ -b & -c & 0\end{array}\right)$ is a skew-symmetric matrix.
Reason (R) : A square matrix $A=\left(a_{i j}\right)$ of order $m$ is said to be skew-symmetric if $A^T=-A$.
- ✓
Both (A) and (R) are true and (R) is the correct explanation of (A).
- B
Both (A) and (R) are true but (R) is not the correct explanation of (A).
- C
(A) is true but (R) is false.
- D
(A) is false but (R) is true.
AnswerCorrect option: A. Both (A) and (R) are true and (R) is the correct explanation of (A).
(a) : $A=\left(\begin{array}{ccc}0 & a & b \\ -a & 0 & c \\ -b & -c & 0\end{array}\right) \therefore A^T=\left(\begin{array}{ccc}0 & -a & -b \\ a & 0 & -c \\ b & c & 0\end{array}\right)$
$
\Rightarrow \quad A^T=-A
$
$\therefore \quad$ Assertion and Reason both are true and Reason is correct explanation of Assertion.
View full question & answer→MCQ 191 Mark
Assertion (A) : The matrix $\left(\begin{array}{llll}1 & 0 & 0 & 0 \\ 0 & 2 & 0 & 0 \\ 0 & 0 & 3 & 0\end{array}\right)$ is a diagonal matrix.
Reason (R) : $A=\left(a_{i j}\right)_{m \times m}$ is a square matrix such that entry $a_{i j}=0 \forall i, j$, then $A$ is called diagonal matrix.
- A
Both (A) and (R) are true and (R) is the correct explanation of (A).
- B
Both (A) and (R) are true but (R) is not the correct explanation of (A).
- C
(A) is true but (R) is false.
- ✓
(A) is false but (R) is true.
AnswerCorrect option: D. (A) is false but (R) is true.
(d) : The given matrix having order $3 \times 4$.
$\therefore \quad$ Given matrix is not a square matrix. Diagonal exist only in the square matrix.
$\therefore \quad$ Assertion is false.
On the other side, Reason satisfies the condition of diagonal matrix.
$\therefore \quad$ Assertion is false but Reason is true.
View full question & answer→MCQ 201 Mark
For any square matrix $A$ with real number entries, consider the following statements.
Assertion (A) : $A+A^{\prime}$ is a symmetric matrix.
Reason (R): $A-A^{\prime}$ is a skew-symmetric matrix.
- A
Both (A) and (R) are true and (R) is the correct explanation of (A).
- ✓
Both (A) and (R) are true but (R) is not the correct explanation of (A).
- C
(A) is true but (R) is false.
- D
(A) is false but (R) is true.
AnswerCorrect option: B. Both (A) and (R) are true but (R) is not the correct explanation of (A).
(b) : Let $B=A+A^{\prime}$, then
$
B^{\prime}=\left(A+A^{\prime}\right)^{\prime}=A^{\prime}+\left(A^{\prime}\right)^{\prime}=A^{\prime}+A=A+A^{\prime}=B
$
Therefore, $B=A+A^{\prime}$ is a symmetric matrix.
Now, let $C=A-A^{\prime}$
$
C^{\prime}=\left(A-A^{\prime}\right)^{\prime}=A^{\prime}-\left(A^{\prime}\right)^{\prime}=A^{\prime}-A=-\left(A-A^{\prime}\right)=-C
$
Therefore, $C=A-A^{\prime}$ is a skew-symmetric matrix.
View full question & answer→MCQ 211 Mark
Assertion $(A)$ : If $A=\frac{1}{3}\left[\begin{array}{ccc}1 & -2 & 2 \\ -2 & 1 & 2 \\ -2 & -2 & -1\end{array}\right]$, then $A\left(A^T\right)=I$
Reason $(R)$ : For any square matrix $A,\left(A^T\right)^T=A$
- A
Both $(A)$ and $(R)$ are true and $(R)$ is the correct explanation of $(A)$.
- ✓
Both $(A)$ and $(R)$ are true but $(R)$ is not the correct explanation of $(A)$.
- C
$(A)$ is true but $(R)$ is false.
- D
$(A)$ is false but $(R)$ is true.
AnswerCorrect option: B. Both $(A)$ and $(R)$ are true but $(R)$ is not the correct explanation of $(A)$.
$\because A A^T=\frac{1}{3}\left[\begin{array}{ccc}1 & -2 & 2 \\ -2 & 1 & 2 \\ -2 & -2 & -1\end{array}\right] \cdot $
$\frac{1}{3}\left[\begin{array}{ccc}1 & -2 & -2 \\ -2 & 1 & -2 \\ 2 & 2 & -1\end{array}\right] $
$=\frac{1}{9}\left[\begin{array}{lll}9 & 0 & 0 \\ 0 & 9 & 0 \\ 0 & 0 & 9\end{array}\right]$
$=\left[\begin{array}{lll}1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{array}\right]=I$
View full question & answer→MCQ 221 Mark
Assertion $(A) : A=\left[\begin{array}{ll}2 & 3 \\ 1 & 4\end{array}\right], B=\left[\begin{array}{ll}1 & 0 \\ 0 & 1\end{array}\right]$, then $\ce{(A + B)^2 = A^2 + B^2 + 2AB}$.
Reason $(R):$ For the matrices $A$ and $B$ given in assertion, $\text{AB=BA}$.
- ✓
Both $(A)$ and $(R)$ are true and $(R)$ is the correct explanation of $(A).$
- B
Both $(A)$ and $(R)$ are true but $(R)$ is not the correct explanation of $(A).$
- C
$(A)$ is true but $(R)$ is false.
- D
$(A)$ is false but $(R)$ is true.
AnswerCorrect option: A. Both $(A)$ and $(R)$ are true and $(R)$ is the correct explanation of $(A).$
$\text{AB=AI=A}$ and $\text{BA=IA=A}$
$\Rightarrow \text{AB=BA}$
Consequently, $\ce{(A + B)^2=(A + B)(A + B)}$
$=\ce{A(A + B) + B(A + B)=A^2 + AB + BA + B^2}$
$=\ce{A^2 + AB + AB + B^2=A^2 + 2AB + B^2}$
View full question & answer→MCQ 231 Mark
Assertion (A) : If $\left[\begin{array}{cc}x y & 4 \\ z+5 & x+y\end{array}\right]=\left[\begin{array}{cc}4 & w \\ 0 & 4\end{array}\right]$, then $x=2, y=2, z=-5$ and $w=4$.
Reason (R) : Two matrices are equal, if their orders are same and their corresponding elements are equal.
- ✓
Both (A) and (R) are true and (R) is the correct explanation of (A).
- B
Both (A) and (R) are true but (R) is not the correct explanation of (A).
- C
(A) is true but (R) is false.
- D
(A) is false but (R) is true.
AnswerCorrect option: A. Both (A) and (R) are true and (R) is the correct explanation of (A).
(a) : $\left[\begin{array}{cc}x y & 4 \\ z+5 & x+y\end{array}\right]=\left[\begin{array}{cc}4 & w \\ 0 & 4\end{array}\right]$
On equating the corresponding elements, we get
$
x y=4, w=4, z+5=0 \text { and } x+y=4
$
On solving these equations, we get $x=2, y=2, z=-5$ and $w=4$. Also, the two matrices are equal, if their orders are same and their corresponding elements are equal.
View full question & answer→MCQ 241 Mark
Assertion (A) : $B=\left[\begin{array}{llll}-\frac{1}{2} & \sqrt{5} & 2 & 3\end{array}\right]_{1 \times 4}$ is a row matrix.
Reason (R): If $B=\left[b_{i j}\right]_{1 \times n}$ is a row matrix, then its order is $n \times 1$.
- ✓
Both (A) and (R) are true and (R) is the correct explanation of (A).
- B
Both (A) and (R) are true but (R) is not the correct explanation of (A).
- C
(A) is true but (R) is false.
- D
(A) is false but (R) is true.
AnswerCorrect option: A. Both (A) and (R) are true and (R) is the correct explanation of (A).
(a) : $B=\left[\begin{array}{llll}-\frac{1}{2} & \sqrt{5} & 2 & 3\end{array}\right]_{1 \times 4}$ is a row matrix. In general, $B=\left[b_{i j}\right]_{1 \times n}$ is a row matrix of order $1 \times n$.
View full question & answer→MCQ 251 Mark
Assertion (A): $\left[\begin{array}{lll}3 & 0 & 0 \\ 0 & 4 & 0 \\ 0 & 0 & 7\end{array}\right]$ is a diagonal matrix.
Reason (R): $A=\left[a_{i j}\right]_{n \times n}$ is a square matrix such that $a_{i j}=0, \forall i \neq j$, then $A$ is called diagonal matrix.
- ✓
Both (A) and (R) are true and (R) is the correct explanation of (A).
- B
Both (A) and (R) are true but (R) is not the correct explanation of (A).
- C
(A) is true but (R) is false.
- D
(A) is false but (R) is true.
AnswerCorrect option: A. Both (A) and (R) are true and (R) is the correct explanation of (A).
(a): If $A=\left[a_{i j}\right]_{n \times n}$ is a square matrix such that $a_{i j}=0$ for $i \neq j$, then $A$ is called diagonal matrix. Thus, the given statement is true and $A=\left[\begin{array}{lll}3 & 0 & 0 \\ 0 & 4 & 0 \\ 0 & 0 & 7\end{array}\right]$ is a diagonal matrix.
View full question & answer→MCQ 261 Mark
Assertion (A) : Scalar matrix $A=\left[a_{i j}\right]$ $=\left\{\begin{array}{ll}k ; & i=j \\ 0 ; & i \neq j\end{array}\right.$ where $k$ is a scalar, is an identity matrix when $k=1$.
Reason (R) : Every identity matrix is not a scalar matrix.
- A
Both (A) and (R) are true and (R) is the correct explanation of (A).
- B
Both (A) and (R) are true but (R) is not the correct explanation of (A).
- ✓
(A) is true but (R) is false.
- D
(A) is false but (R) is true.
AnswerCorrect option: C. (A) is true but (R) is false.
(c) : A scalar matrix $A=\left[a_{i j}\right]=\left\{\begin{array}{ll}k, & i=j \\ 0, & i \neq j\end{array}\right.$ is an identity matrix when $k=1$. But every identity matrix is clearly a scalar matrix.
View full question & answer→