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Determinants and Matrices — Maths STD 11 Science — Question

Maharashtra BoardEnglish MediumSTD 11 ScienceMathsDeterminants and Matrices2 Marks
Question
Show that
$\begin{aligned}
& \left|\begin{array}{ccc}
101 & 202 & 303 \\
505 & 606 & 707 \\
1 & 2 & 3
\end{array}\right|=0\end{aligned} $
✓

Answer

$\begin{aligned}
& \text { LHS }=\left|\begin{array}{ccc}
101 & 202 & 303 \\
505 & 606 & 707 \\
1 & 2 & 3
\end{array}\right| \\
& \mathrm{R}_1 \rightarrow \mathrm{R}_1-\mathrm{R}_3 \\
& =\left|\begin{array}{ccc}
100 & 200 & 300 \\
505 & 606 & 707 \\
1 & 2 & 3
\end{array}\right| \\
& =\left|\begin{array}{ccc}
100 \times 1 & 100 \times 2 & 100 \times 3 \\
505 & 606 & 707 \\
1 & 2 & 3
\end{array}\right|
\end{aligned}
$

$=100\left|\begin{array}{ccc}1 & 2 & 3 \\ 505 & 606 & 707 \\ 1 & 2 & 3\end{array}\right|$ by using property
$=100 \times 0\left(\mathrm{R}_1\right.$ and $\mathrm{R}_3$ are identical $)$
$=0$

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