Question

Consider a linear system Ax b,and the SVD of the matrix A UXVH (a) please use matrices U, V, 2 to express the pseudo-inverse of the linear system. (b) please show that Av1 1u1, Av2 = 02u2,, Av, a,l,, where ris the rank of the matrix 2 0 (c) If A is a 3x2 matrix A = ( 0 0, calculate its reduced SVD (that is, find its U, 2, V); 0

Answer 1

Griven that Lineas system Ax-b and -the SD of A the matsi A -0EH matias u,v. to express -the PSeuelo- of the lineas System (a) Ose Nerse + ち、uト AA Im AA =In AATA = Imx Amxo Amto A AA Any CAAT* CAA) - In (AAt)A Tm)TA (ATA A)

AV, Gu,, ois the sark of the matone V$ A = UΣ ν"ν AN = Av = she usi Copanals Ci-1,2, AVi LASI Proded A is 3x9 malbix A OI A - O A= vEN A A = engan Nahu , eiqun elo Conesponsing to u ae YOO

(ey definton) OI O O AA 2 00 oot Ho 4,lare eizen Nedas Coaponalng Another Pepedicca basi's to thaS two oo Oo OIO . . A= UEN V Au LAus +8)() (6)