1. (25 points) In this question, you will compare the QR and SVD decomposition of a matrix. Let A [V2/2 V2/2] -V2 V2 (a) Find the QR decomposition for the above matrix (b) Find an SVD decomposition for the matrix A above, i.e. find orthogonal matrices UA, VA and a "diagonal" matrix (in the sense of SVD) EA such that A = UAEAVA (c) For the matrix R which you found in part (a), find an SVD decomposition, i.e. matrices UR, ER, VR such that R = URER*VR (d) In general, suppose A is an n x n matrix with linearly independent columns, and so has a QR decomposition with Q an orthogonal matrix. If we compare the SVD decomposition for R and A, what changes? In other words: what is the relation between the singular values of R and those of A? what is the relation between UR and UA? what is the relation between VR and VA