Evaluate 2&3&-5 7&1&-2 -3&4&1 by two methods. - Vidyadip

Question

Evaluate $\begin{vmatrix}2&3&-5\\7&1&-2\\-3&4&1\end{vmatrix}$ by two methods.

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Answer

We will evaluate the given determinant:

Along the first row.

$|\text{A}|=2\begin{vmatrix}1&-2\\4&1 \end{vmatrix}-3\begin{vmatrix}7&-2\\-3&1\end{vmatrix}-3\begin{vmatrix}7&1\\-3&4\end{vmatrix}$

$=2(1+8)-7(3+20)-3(-6+5)$

$=18-7(23)-3(-1)$

$=21-161$

$=-140$

Along the first column.

$|\text{A}|=\begin{vmatrix}1&-2\\4&1 \end{vmatrix}-7\begin{vmatrix}3&-5\\4&1\end{vmatrix}-3\begin{vmatrix}3&-5\\1&-2\end{vmatrix}$

$=2(1+8)-7(3+20)-3(-6+5)$

$=18-7(23)-3(-1)$

$=18-161+3$

$=21-161$

$=-140$

We can see, the answer is same with both the methods.

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