Assertion (A) : The matrix ( llll 1 & 0 & 0 & 0 0 & 2 & 0 & 0 0 &… - Vidyadip

MCQ

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.

✓

Answer

Correct 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.

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