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Matrices — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsMatrices1 Mark
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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