Find the rank of the matrix
\(A=\left( \begin{matrix} 2 & 4 & 5 \\ 4 & 8 & 10 \\ -6 & -12 & -15 \end{matrix} \right) \)

Find the rank of the matrix \(A=\left( \begin{matrix} 1 & 2 & -4 \\ 2 & -1 & 3 \\ 8 & 1 & 9 \end{matrix}\begin{matrix} 5 \\ 6 \\ 7 \end{matrix} \right) \)

Show that the equations 2x - y + z = 7, 3x + y - 5z = 13, x + y + z = 5 are consistent and have a unique solution.

Show that the equations x + 2y = 3, y - z = 2, x + y + z = 1 are consistent and have infinite sets of solution.

Show that the equations x- 3y + 4z = 3, 2x - 5y + 7z = 6, 3x - 8y + 11z = 1 are inconsistent