Question 3. Define the matrix P by 4/5 0 3/5 P = -3/5 0 4/5 0 1 0 (a) Let v1, . .., Uk ( R". Define what it means that 71, ..., U are orthogonal. (b) Let v1, ... . U. ER". Define what it means that v1, ..., . are orthonormal. (c) Let A be an n x n square matrix. Show that A'A is diagonal if and only if the columns of A are orthogonal to each other. (d) Let A be an n x n square matrix. Show that A'A is the identity matrix if and only if the columns of. A form an orthonormal basis of R". (e) Show that the columns of P form an orthonormal basis of R". (f ) What is the inverse of P? (g) Solve the linear system of equations. Hint, use (f). P T2 C3 2