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Matrics — Maths STD 12 Science — Question

Maharashtra BoardEnglish MediumSTD 12 ScienceMathsMatrics2 Marks
MCQ
If matrix $A=\left[\begin{array}{ll}1 & 2 \\ 4 & 3\end{array}\right]$ such that $A X=I$, then $X=$
  • A
    $\frac{1}{5}\left[\begin{array}{rr}1 & 3 \\ 2 & -1\end{array}\right]$
  • B
    $\frac{1}{5}\left[\begin{array}{rr}4 & 2 \\ 4 & -1\end{array}\right]$
  • ✓
    $\frac{1}{5}\left[\begin{array}{cr}-3 & 2 \\ 4 & -1\end{array}\right]$
  • D
    $\frac{1}{5}\left[\begin{array}{ll}-1 & 2 \\ -1 & 4\end{array}\right]$
✓

Answer

Correct option: C.
$\frac{1}{5}\left[\begin{array}{cr}-3 & 2 \\ 4 & -1\end{array}\right]$
(c) : $\because A=\left[\begin{array}{ll}1 & 2 \\ 4 & 3\end{array}\right]$, such that $A X=I$
$\Rightarrow X=A^{-1} I$
$\because|A|=3-8=-5 \neq 0 \Rightarrow A^{-1}$ exists.
$A^{-1}=\frac{1}{-5}\left[\begin{array}{cc}3 & -2 \\ -4 & 1\end{array}\right]=\frac{1}{5}\left[\begin{array}{cc}-3 & 2 \\ 4 & -1\end{array}\right]$
$\therefore \quad X=\frac{1}{5}\left[\begin{array}{cc}-3 & 2 \\ 4 & -1\end{array}\right]\left[\begin{array}{ll}1 & 0 \\ 0 & 1\end{array}\right]=\frac{1}{5}\left[\begin{array}{cc}-3 & 2 \\ 4 & -1\end{array}\right]$

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