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Matrices (p-1) — Maths (commerce) STD 12 Commerce / Arts — Question

Maharashtra BoardEnglish MediumSTD 12 Commerce / ArtsMaths (commerce)Matrices (p-1)3 Marks
Question
Transform $\left[\begin{array}{ccc}1 & -1 & 2 \\ 2 & 1 & 3 \\ 3 & 2 & 4\end{array}\right]$ into an upper triangularmatrix by suitable row transformations.
✓

Answer

Let $A=\left(\begin{array}{rrr}1 & -1 & 2 \\ 2 & 1 & 3 \\ 3 & 2 & 4\end{array}\right)$
By $R_2-2 R_1$ and $R_3-3 R_1$, we get
$
A \sim\left(\begin{array}{rrr}
1 & -1 & 2 \\
0 & 3 & -1 \\
0 & 5 & -2
\end{array}\right)
$
By $\left(\frac{1}{3}\right) R_2$, we get
$
A \sim\left[\begin{array}{rrr}
1 & -1 & 2 \\
0 & 1 & -\frac{1}{3} \\
0 & 5 & -2
\end{array}\right]
$
By $R_3-5 R_2$, we get
$
A \sim\left[\begin{array}{rrr}
1 & -1 & 2 \\
0 & 1 & -\frac{1}{3} \\
0 & 0 & -\frac{1}{3}
\end{array}\right]
$
This is an upper triangular matrix.

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