1 1 1 3- Let A = 31 31 g . Use the Householder algorithm to find a 3 x 3 upper triangular matrix R and unit vectors 111, 112, and 1 3 7 113 such that...

This is a question from Math class which is numerical linear algebra.

— 1 —1 13- Let A = 31 31 g . Use the Householder algorithm to find a 3 x 3 upper triangular matrix R and unit vectors 111, 112, and1 3 7113 such that if we let 1 0 I 0Q1=I4x472u1llia Q2: [ ] , Q3: [2324x4 0 1567211211; 12x272u3u§ 4x4 and define Q to be the 4 x 3 matrix whose columns are the first 3 columns of Q’fQ; Q5, then A = QR. You are asked to find R, 111,112, and 113. (Show all of your work; no credit will be given for unsupported answers.)