Evaluate : | rrr 3 & -4 & 5 1 & 1 & -2 2 & 3 & -1 | - Vidyadip

Question

Evaluate : $\left|\begin{array}{rrr}3 & -4 & 5 \\ 1 & 1 & -2 \\ 2 & 3 & -1\end{array}\right|$

✓

Answer

$
\begin{aligned}
\left|\begin{array}{rrr}
3 & -4 & 5 \\
1 & 1 & -2 \\
2 & 3 & -1
\end{array}\right|= & 3\left|\begin{array}{ll}
1 & -2 \\
3 & -1
\end{array}\right|-(-4)\left|\begin{array}{rr}
1 & -2 \\
2 & -1
\end{array}\right| \\
& +5\left|\begin{array}{ll}
1 & 1 \\
2 & 3
\end{array}\right| \\
& =3(-1+6)+4(-1+4)+5(3-2) \\
& =3 \times 5+4 \times 3+5 \times 1 \\
& =15+12+5 \\
& =32
\end{aligned}
$

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