Evaluate determinant along second column

$\left|\begin{array}{ccc}1& -1& 2\\ 3& 2& -2\\ 0& 1& -2\end{array}\right|$

Evaluate 

$\left|\begin{array}{ccc}2& 3& 5\\ 400& 600& 1000\\ 48& 47& 18\end{array}\right|$

Evaluate by using properties 

 $\left|\begin{array}{ccc}101& 102& 103\\ 106& 107& 108\\ 1& 2& 3\end{array}\right|$ 

Find minor and cofactor of elements of the determinant.

$\left|\begin{array}{ccc}-1& 0& 4\\ -2& 1& 3\\ 0& -4& 2\end{array}\right|$

Find minor and cofactor of elements of the determinant.

$\left|\begin{array}{ccc}1& -1& 2\\ 3& 0& -2\\ 1& 0& 3\end{array}\right|$

Find the value of $\mathrm{x}$ if 

$\left|\begin{array}{ccc}1& 4& 20\\ 1& -2& -5\\ 1& 2\mathrm{x}& 5{\mathrm{x}}^2\end{array}\right|=0$

Find the value of $\mathrm{x}$ if

$\left|\begin{array}{ccc}1& 2\mathrm{x}& 4\mathrm{x}\\ 1& 4& 16\\ 1& 1& 1\end{array}\right|=0$

By using properties of determinant prove that

 $\left|\begin{array}{ccc}\mathrm{x}+\mathrm{y}& \mathrm{y}+\mathrm{z}& \mathrm{z}+\mathrm{x}\\ \mathrm{z}& \mathrm{x}& \mathrm{y}\\ 1& 1& 1\end{array}\right|=0$

Without expanding determinant show that

$\left|\begin{array}{ccc}\mathrm{b}+\mathrm{c}& \mathrm{bc}& {\mathrm{b}}^2{\mathrm{c}}^2\\ \mathrm{c}+\mathrm{a}& \mathrm{ca}& {\mathrm{c}}^2{\mathrm{a}}^2\\ \mathrm{a}+\mathrm{b}& \mathrm{ab}& {\mathrm{a}}^2{\mathrm{b}}^2\end{array}\right|=0$