An orthogonal basis for the column space of matrix A is (v,, v2, v3). Use this orthogonal basis to 1 2 5 1 -1 2 find a QR factorization of matrix A. -1 -2 1 - 1 1 4 A = 4 3 v = V2 = 4 V3 1 4 4 1 1 -1 1 4 8 1 1 3 =R=D (Type exact answers, using radicals as needed.)

Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter5: Orthogonality
Section5.3: The Gram-schmidt Process And The Qr Factorization
Problem 23EQ
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An orthogonal basis for the column space of matrix A is {v1, v2, V3). Use this orthogonal basis to
1
25
- 1
2
find a QR factorization of matrix A.
-1 -2 1
4
A =
4 3
V, =
4
V3 =
- 1
4 4
1
- 1
1
4 8
1
1
3
R=
Q =
(Type exact answers, using radicals as needed.)
Transcribed Image Text:An orthogonal basis for the column space of matrix A is {v1, v2, V3). Use this orthogonal basis to 1 25 - 1 2 find a QR factorization of matrix A. -1 -2 1 4 A = 4 3 V, = 4 V3 = - 1 4 4 1 - 1 1 4 8 1 1 3 R= Q = (Type exact answers, using radicals as needed.)
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