Let Q be an n n orthogonal matrix. Show that (a) _Q_2 = 1 (b) cond2(Q) = 1 (c) for any b Rn, the relative error in the solution of Qx = b is equal to the relative residual; that is, _e_2 _x_2 = _r_2 _b_2 4

Topic=YellowSubtopic=Green Multivariable Calculus and Matrix Algebra Orthogonal Set, Orthonormal Set Definition: a) Suppose u is a subset of nonzero vectors in an inner product space V if u,u=0 whenever I doesnâ€™t equal j we say the u is orthogonal b) Suppose u is an orthogonal set If u=1 for every k then u is called orthonormal set Theorem: an orthogonal set is L.I...