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Matrices — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsMatrices1 Mark
MCQ
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.
✓

Answer

Correct 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.

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