Question

Evaluate \[\Delta=\begin{vmatrix}1&2&4\\-1&3&0\\4&1&0\end{vmatrix}\] by expansion along \[C_3\].

Options

• \[-52\]

• \[13\]

• \[52\]

• \[-13\]

Answer 1

Expansion along \[C_3\] leaves \[4\begin{vmatrix}-1&3\\4&1\end{vmatrix}\], because the other two terms contain zero. Since \[(-1)(1)-3(4)=-13\], the determinant is \[4(-13)=-52\].