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Matrics — Maths STD 12 Science — Question

Maharashtra BoardEnglish MediumSTD 12 ScienceMathsMatrics2 Marks
MCQ
The upper triangular matrix of the matrix $\left[\begin{array}{ccc}1 & -1 & 2 \\ 2 & 1 & 3 \\ 3 & 2 & 4\end{array}\right]$ is
  • ✓
    $\left[\begin{array}{ccc}1 & -1 & 2 \\ 0 & 3 & -1 \\ 0 & 0 & \frac{-1}{3}\end{array}\right]$
  • B
    $\left[\begin{array}{ccc}1 & 1 & -2 \\ 0 & 3 & -1 \\ 0 & 0 & \frac{-1}{3}\end{array}\right]$
  • C
    $\left[\begin{array}{ccc}\frac{-1}{3} & 0 & 0 \\ 3 & -1 & 0 \\ -1 & 2 & 0\end{array}\right]$
  • D
    $\left[\begin{array}{ccc}1 & 1 & 2 \\ 0 & -3 & -1 \\ 0 & 0 & \frac{-1}{3}\end{array}\right]$
✓

Answer

Correct option: A.
$\left[\begin{array}{ccc}1 & -1 & 2 \\ 0 & 3 & -1 \\ 0 & 0 & \frac{-1}{3}\end{array}\right]$
(A) Let $A=\left[\begin{array}{ccc}1 & -1 & 2 \\ 2 & 1 & 3 \\ 3 & 2 & 4\end{array}\right]$
Applying $R _2 \rightarrow R _2-2 R _1$ and $R _3 \rightarrow R _3-3 R _1$,
$A \sim\left[\begin{array}{ccc}1 & -1 & 2 \\ 0 & 3 & -1 \\ 0 & 5 & -2\end{array}\right]$
Applying $R _3 \rightarrow R _3-\left(\frac{5}{3}\right) R _2$,
$A \sim\left[\begin{array}{ccc}1 & -1 & 2 \\ 0 & 3 & -1 \\ 0 & 0 & -\frac{1}{3}\end{array}\right]$
which is an upper triangular matrix.

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