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Question: Answered & Verified by Expert
If $\mathrm{A}=\left[\begin{array}{ccc}1 & 0 & -2 \\ 2 & -3 & 4\end{array}\right]$, then the matrix $\mathrm{X}$ for which $2 \mathrm{X}+3 \mathrm{~A}=$ 0 holds true is
MathematicsMatricesNDANDA 2015 (Phase 2)
Options:
  • A $\left[\begin{array}{ccc}-\frac{3}{2} & 0 & -3 \\ -3 & -\frac{9}{2} & -6\end{array}\right]$
  • B $\left[\begin{array}{ccc}\frac{3}{2} & 0 & -3 \\ 3 & -\frac{9}{2} & -6\end{array}\right]$
  • C $\left[\begin{array}{ccc}\frac{3}{2} & 0 & 3 \\ 3 & \frac{9}{2} & 6\end{array}\right]$
  • D $\left[\begin{array}{ccc}-\frac{3}{2} & 0 & 3 \\ -3 & \frac{9}{2} & -6\end{array}\right]$
Solution:
2106 Upvotes Verified Answer
The correct answer is: $\left[\begin{array}{ccc}-\frac{3}{2} & 0 & 3 \\ -3 & \frac{9}{2} & -6\end{array}\right]$
$\because 2 X+3 A=0$
$\Rightarrow x=\frac{-3}{2} A$
$\Rightarrow x=\frac{-3}{2}\left[\begin{array}{ccc}1 & 0 & -2 \\ 2 & -3 & 4\end{array}\right]$
$\Rightarrow X=\left[\begin{array}{ccc}-\frac{3}{2} & 0 & 3 \\ -3 & \frac{9}{2} & -6\end{array}\right]$

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