5. Let T: R³ R³ where T(u) reflects the vector u across the plane 2x - 3y + z = 0 with the weighted inner product (u, v) = 2u1 0₁ +42₂ +33 A. (7 pts) Find the matrix transformation that represent this transformation by writing it as a product of PDP, where P is an orthogonal matrix and D is a diagonal matrix matrices A B. (4 pts) Find a basis for ker(T) and T(R³). C. (3 pts) Find the eigenvalues of the matrix A. 5. Let T: R³ R³ where T(u) reflects the vector u across the plane 2x - 3y + z = 0 with the weighted inner product (u, v) = 2u1v₁ +₂₂+33 A. (7 pts) Find the matrix transformation that represent this transformation by writing it as a product of PDP', where P is an orthogonal matrix and D is a diagonal matrix matrices A = B. (4 pts) Find a basis for ker(T) and T(R³). C. (3 pts) Find the eigenvalues of the matrix A. 5. Let T: R³ R³ where T(u) reflects the vector u across the plane 2x - 3y + z = 0 with the weighted inner product (u, v) = 2u1v₁ +₂₂+33 A. (7 pts) Find the matrix transformation that represent this transformation by writing it as a product of PDP', where P is an orthogonal matrix and D is a diagonal matrix matrices A = B. (4 pts) Find a basis for ker(T) and T(R³). C. (3 pts) Find the eigenvalues of the matrix A.