The system of equations

$$2x + y - 3z = 5$$

$$3x - 2y + 2z = 5$$

and $$5x - 3y - z = 16$$

If u, v and w (all positive) are the pth, qth, and rth terms of a GP, then the determinant of the matrix $$\left( {\matrix{ {\ln \,u} & p & 1 \cr {\ln v} & q & 1 \cr {\ln w} & r & 1 \cr } } \right)$$ is

Let matrix B be the adjoint of a square matrix A, I be the identity matrix of same order as A. If k($$\ne$$ 0) is the determinant of the matrix A, then what is AB equal to?

What is the determinant of the matrix $$\left( {\matrix{ x & y & {y + z} \cr z & x & {z + x} \cr y & z & {x + y} \cr } } \right)$$ ?