Solve: 2x + 3y = 10, x + 6y = 4 using Cramer's rule.

Solve: 3x+ay = 4, 2x + ay = 2, a ≠ 0 by Cramer's rule.

Under what conditions will the rank of the matrix \(\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & h-2 & 2 \\ \begin{matrix} 0 \\ 0 \end{matrix} & \begin{matrix} 0 \\ 0 \end{matrix} & \begin{matrix} h+2 \\ 3 \end{matrix} \end{matrix} \right] \) be less than 3?

Verify that (A^-1)^T = (A^T)^-1 for A =\(\left[ \begin{matrix} -2 & -3 \\ 5 & -6 \end{matrix} \right] \).

Solve: x + y + 3z = 4, 2x + 2y + 6z = 7, 2x + y +  z = 10.