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Matrices — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsMatrices1 Mark
MCQ
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.
✓

Answer

Correct 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.

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