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MAT2114 Homework §5.3 Due Date: 29 April 2022 Name: Instructions: Answer the following questions, showing ALL your work and writing neatly. This assignment is due to Canvas by 11:59pm on the date...

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MAT2114 Homework §5.3
Due Date: 29 April 2022 Name:
Instructions: Answer the following questions, showing ALL your work and writing neatly. This
assignment is due to Canvas by 11:59pm on the date above. Group work is allowed and
encouraged, but each group member must write up their own solutions.
1. In §5.3 WebAssign, Problem #5, you’re asked to find an orthonormal basis for the column
space of a 3 × 3 matrix (call it A).
(a) Find the co
esponding QR-factorization of A.
(For an added challenge, can you find a QR-factorization for which det(Q) = 1?)
(b) Show that RQ is similar to A.
1

Answered Same Day Apr 29, 2022

Solution

Rajeswari answered on Apr 29 2022
97 Votes
We are given already u1 u2 and u3 as columns of orthonormal basis
We have a1 =u1 =(0,1,1): a2 = (3,0,3) and a3=(-1,-1,0)
Our job is to find e1,e2,e3
We get e1=u1/||u1|| =ro
Next u2 = a2-proj of e1 on a2 =
So we get e2=unit vectoralong e1 =
U3 = a3-proj of e1 on a3-proj of e2 on a3 =
Thus Q...
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