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Determinants — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsDeterminants1 Mark
MCQ
Let $A=\left[\begin{array}{ccc}1 & 0 & a \\ 2 & 3 & b \\ -3 & 1 & c\end{array}\right], B=\left[\begin{array}{ccc}1 & 0 & x \\ 2 & 3 & y \\ -3 & 1 & z\end{array}\right]$
and $C=\left[\begin{array}{ccc}1 & 0 & a+x \\ 2 & 3 & b+y \\ -3 & 1 & c+z\end{array}\right]$.
Assertion (A) : $\operatorname{det} A+\operatorname{det} B=\operatorname{det} C$.
Reason (R) : $A+B=C$.
  • 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).
  • ✓
    (A) is true but (R) is false.
  • D
    (A) is false but (R) is true.
✓

Answer

Correct option: C.
(A) is true but (R) is false.
(c) : Clearly $A+B \neq C$. Hence, reason is wrong.
However, by a property of determinants, $\operatorname{det} C=\operatorname{det} A+\operatorname{det} B$.
$\therefore \quad$ Assertion is correct statement but reason is wrong statement.

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