Question: Example.ConsiderthematrixA= 1 1 1 0 .UsingAlgorithmQR(Householder): k=1: u=a1= 1 1 v=u+sign(u1)u 2e1= 1 1 + 2 0 = 1+ 2 1 w= 1 v 2

Example.ConsiderthematrixA= 1 1 1 0 .UsingAlgorithmQR(Householder): k=1: u=a1= 1 1 v=u+sign(u1)u 2e1= 1 1 + 2 0 = 1+ 2 1 w= 1 v 2 v= 1 (1+ 2)2+12 1+ 2 1 = 1 2 2+ 2 1+ 2 1 Hk=I 2wwT= 1 0 0 1 2 2(2+ 2) 3+2 2 1+ 2 1+ 2 1 = 1 2 1 1 1 1 R=HkA= 1 2 1 1 1 1 1 1 1 0 = 1 2 2 1 0 1 Q=IHk=Hk= 1 2 1 1 1 1 Hence,wehaveQ= 1 2 1 1 1 1 andR= 1 1 1 0 = 1 2 2 1 0 1 .

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