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Matrics — Maths STD 12 Science — Question

Maharashtra BoardEnglish MediumSTD 12 ScienceMathsMatrics2 Marks
MCQ
If $A=\left[\begin{array}{cc}x & -2 \\ 3 & 7\end{array}\right]$ and $A^{-1}=\left[\begin{array}{cc}\frac{7}{34} & \frac{1}{17} \\ \frac{-3}{34} & \frac{2}{17}\end{array}\right]$, then the value of $x$ is
  • A
    2
  • B
    3
  • C
    -4
  • ✓
    4
✓

Answer

Correct option: D.
4
(D) Since $AA ^{-1}= I$,
$\left[\begin{array}{cc}x & -2 \\ 3 & 7\end{array}\right]\left[\begin{array}{cc}\frac{7}{34} & \frac{1}{17} \\ \frac{-3}{34} & \frac{2}{17}\end{array}\right]=\left[\begin{array}{ll}1 & 0 \\ 0 & 1\end{array}\right]$
$\Rightarrow\left[\begin{array}{cc}\frac{7 x+6}{34} & \frac{x-4}{17} \\ 0 & 1\end{array}\right]=\left[\begin{array}{ll}1 & 0 \\ 0 & 1\end{array}\right]$
By equality of matrices,
$\frac{x-4}{17}=0 \Rightarrow x-4=0$
$\Rightarrow x=4$

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