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Matrics — Maths STD 12 Science — Question

Maharashtra BoardEnglish MediumSTD 12 ScienceMathsMatrics2 Marks
MCQ
If $\left[\begin{array}{ccc}1 & 3 & -2 \\ -3 & 0 & -5 \\ 2 & 5 & 0\end{array}\right]= A \left[\begin{array}{lll}1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{array}\right]$
then $C _2 \rightarrow C _2-3 C _1$ and $C _3 \rightarrow C _3+2 C _1$ gives
  • A
    $\left[\begin{array}{ccc}1 & 0 & 0 \\ 3 & -9 & 11 \\ -2 & 1 & 4\end{array}\right]=A\left[\begin{array}{ccc}-1 & 3 & 2 \\ 0 & -1 & 0 \\ 0 & 0 & -1\end{array}\right]$
  • B
    $\left[\begin{array}{ccc}1 & 0 & 0 \\ -3 & -1 & -4 \\ 2 & -9 & 11\end{array}\right]-A\left[\begin{array}{ccc}1 & -3 & 2 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{array}\right]$
  • C
    $\left[\begin{array}{ccc}1 & 0 & 0 \\ -3 & 1 & 4 \\ -2 & 9 & -11\end{array}\right]=A\left[\begin{array}{ccc}-1 & 3 & 2 \\ 0 & -1 & 0 \\ 0 & 0 & -1\end{array}\right]$
  • ✓
    $\left[\begin{array}{ccc}1 & 0 & 0 \\ -3 & 9 & -11 \\ 2 & -1 & 4\end{array}\right]=A\left[\begin{array}{ccc}1 & -3 & 2 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{array}\right]$
✓

Answer

Correct option: D.
$\left[\begin{array}{ccc}1 & 0 & 0 \\ -3 & 9 & -11 \\ 2 & -1 & 4\end{array}\right]=A\left[\begin{array}{ccc}1 & -3 & 2 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{array}\right]$
(D) $\left[\begin{array}{ccc}1 & 3 & -2 \\ -3 & 0 & -5 \\ 2 & 5 & 0\end{array}\right]= A \left[\begin{array}{lll}1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{array}\right]$
Applying $C _2 \rightarrow C _2-3 C _1$ and $C _3 \rightarrow C _3+2 C _1$,
$\left[\begin{array}{ccc}1 & 3-3 & -2+2 \\ -3 & 0+9 & -5-6 \\ 2 & 5-6 & 0+4\end{array}\right]= A \left[\begin{array}{lll}1 & 0-3 & 0+2 \\ 0 & 1-0 & 0+0 \\ 0 & 0-0 & 1+0\end{array}\right]$
$\Rightarrow\left[\begin{array}{ccc}1 & 0 & 0 \\ -3 & 9 & -11 \\ 2 & -1 & 4\end{array}\right]= A \left[\begin{array}{ccc}1 & -3 & 2 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{array}\right]$

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