Assertion (A): [ lll 3 & 0 & 0 0 & 4 & 0 0 & 0 & 7 ] is a diagona… - Vidyadip

Question

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.

✓

Answer

(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.

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "Assertion (A) & Reason (B) MCQ" from Matrices→Matrices — all question types→MATHS STD 12 Science question papers→Rajasthan Board STD 12 Science question papers→Rajasthan Board question paper generator→

Similar questions

Directions: In the following questions, the Assertions $(A)$ and Reason$(s) (R)$ have been put forward. Read both the statements carefully and choose the correct alternative from the following:
Assertion: $\text{f}(\text{x})=\begin{cases}\text{x}^2\sin\big(\frac{1}{\text{x}}\big), &\text{x}=0\\0, &\text{x}=0\end{cases}$ is continuous at $x = 0.$
Reason: Both $\text{h}(\text{x})=\text{x}^2,\text{g}(\text{x})=\begin{cases}\text{x}^2\sin\big(\frac{1}{\text{x}}\big), &\text{x}=0\\0, &\text{x}=0\end{cases}$ are continuous at $x = 0.$

Directions: In the following questions, a statement of assertion $(A)$ is followed by a statement of reason $(R).$ Mark the correct choice as:
Assertion: The minor of the element $3$ in the matrix $\begin{bmatrix}2&3&1\\0&-2&4\\2&1&5\end{bmatrix}$ is $8$.
Reason: Minor of an element $a_{ij}$ of a matrix is the determinant obtained by deleting its $j^{th}$ row and $i^{th}$ column.

Assertion (A) : Bag I contains 3 red and 4 black balls while another bag II contains 5 red and 6 black balls. One ball is drawn at random from one of the bags and it is found to be red. Then, the probability that it was drawn from bag II is $\frac{35}{68}$.
Reason (R) : By Bayes' theorem,
$
\begin{array}{r}
P\left(\frac{E_1}{A}\right)=\frac{P\left(E_1\right) \cdot P\left(A / E_1\right)}{P\left(E_1\right)\left(A \mid E_1\right)+P\left(E_1\right) \cdot P\left(A \mid E_2\right)+P\left(E_1\right) P\left(A \mid E_3\right)}
\end{array}
$

Assertion (A) : A differential equation of the form $y f(x y) d x+x g(x y) d y=0$ can be converted into homogeneous differential equation by substituting $x y=t$
Reason (R) : A differential equation is called homogeneous if $f(\lambda x, \lambda y)=\lambda^0 f(x, y)$.

Directions: In these questions, a statement of Assertion is followed by a statement of Reason is given.Choose the correct answer out of the following choices:
Assertion: The area bounded by the curves $\text{y}^2 = 4\text{a}^2(\text{x} — 1) $ and lines $\text{x}=1$ and $\text{y}=4$ a is $\frac{8\text{a}}{3}\text{sq.units}$
Reason: The area enclosed between the parabola $\text{y}=\text{x}^2-\text{x}+2$ and the line $\text{y}=\text{x+2}$ is $\frac{4}{3}\text{ sq.units}$

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.
Both A and R are true but R is not the correct explanation of A.
A is true but R is false.
A is false but R is true.
Both A and R are false.

Assertion (A) : Integrating factor of $\left(1+x^2\right) \frac{d y}{d x}+x y=\frac{1}{2 x}$ is given by $\sqrt{1+x^2}$.
Reason (R) : Integrating factor of $\frac{d y}{d x}+P(x) \cdot y=Q(x)$ is $e^{\int P(x) d x}$.

Assertion (A) : All trigonometric functions have their inverses over their respective domains.
Reason (R) : The inverse of $\tan ^{-1} x$ exists for some $x \in R$.

Directions: In the following questions, the Assertions (A) and Reason(s) (R) have been put forward. Read both the statements carefully and choose the correct alternative from the following:
Assertion (A) f(x) = [x] greatest integer function is not differentiable at x = 2
Reason(R) The greatest integer function is not continuous at any integer

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.
A is true but R is false
A is false but R is true

Assertion (A) : Both $\sin x$ and $\cos x$ are decreasing functions in $\left(\frac{\pi}{2}, \pi\right)$.
Reason (R): If a differentiable function decreases in $(a, b)$, then its derivative also decreases in $(a, b)$.