Assignment 2 Deadline: 2023-02-21 *************************************************************************** 1. Let u = [1.1, 1,1] and S = span{v1.vQ,V3,V4}, where V1 = [0,3,2,2], V2 = [1,1,0,1], V3 = [3,0,2,1], V4 = [1,2,2,1]. (a) Find a subset of {V1,V2, V3. V4} that forms a basis for the space S. (b) Express each vector which is not in the basis as a linear combination of the basis vectors. (c) Find the orthogonal projection of 11 onto 5 and the component of u orthogonal to S. 2. Find an orthogonal basis for R3 that contains a vector V1 = [0, 2, 3]. 3. Find the QRdecomposition of the matrix. 1 *1 4 1 2 ) 0 1 (b) 1 4 '2 a 1 4 2 1 4 l *1 0 4. Find the least squares solution of each linear system Ax = b1 and nd the orthogonal projection of b on the column space of A. 2 0 5 3 1 l 1 1 1 (a)A= _1 1 ,b: _1 (b)A: .b: 3 1 *1 1 *2 l *1 2 3 5. Consider the bases B : {u1,u2} and C : {V1, v2} for R2, Where u1 : [1,0], u2 : [111]; V1 :[1~*1iy V2 : [Q11- (a) Find the transition matrix P from B to C, and the transition matrix Q from C to B. (b) Find the coordinate vector [X]C if x : [3, *4]. (c) Find [xhg according to the coordinate vector [x]c in (b)