Solve\(\left[ \begin{matrix} { x }^{ 2 } \\ { y }^{ 2 } \end{matrix} \right] -3\left[ \begin{matrix} x \\ 2y \end{matrix} \right] =\left[ \begin{matrix} -2 \\ 9 \end{matrix} \right] \)

Find the value of x such that [1 \(\times\) 1]\(\left[ \begin{matrix} 1 & 3 & 2 \\ 2 & 5 & 1 \\ 15 & 3 & 2 \end{matrix} \right] \left[ \begin{matrix} 1 \\ 2 \\ x \end{matrix} \right] =0\)

Using properties of determinant, show that \(\triangle =\left| \begin{matrix} { cosec }^{ 2 }\theta & -{ cot }^{ 2 }\theta & 1 \\ { cot }^{ 2 }\theta & -cose{ c }^{ 2 }\theta & -1 \\ 42 & 40 & 2 \end{matrix} \right| =0\)

Prove that \(\left| \begin{matrix} 1 & 1+p & 1+p+q \\ 2 & 3+2p & 4+4p+2q \\ 3 & 6+3p & 10+6p+3q \end{matrix} \right| =1\)

Prove that \(\left| \begin{matrix} 1 & 1 & 1 \\ 1 & 1+x & 1 \\ 1 & 1 & 1+y \end{matrix} \right| =xy\)