An orthogonal basis for the column space of matrix A is {V1, V2, V3}. Use this orthogonal basis to find a QR factorization of matrix A. 1 2 4 1 2 2 -1 -2 1 - 1 3 A = 4 3 V1 = V2 = 4 V3 = - 1 6 4 1 2 - 2 1 6 9 1 2 3 Q = R = (Type exact answers, using radicals as needed.)

Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter5: Orthogonality
Section5.4: Orthogonal Diagonalization Of Symmetric Matrices
Problem 27EQ
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An orthogonal basis for the column space of matrix A is
1
2 4
2
2
{V1, V2, V3}. Use this orthogonal basis to find a QR
- 1 -2 1
- 1
2
3
factorization of matrix A
A =
4 3
V1 =
V2:
4
V3
- 1
1
6 4
1
6 9
1
2
3
Q=.
R =
(Type exact answers, using radicals as needed.)
Transcribed Image Text:An orthogonal basis for the column space of matrix A is 1 2 4 2 2 {V1, V2, V3}. Use this orthogonal basis to find a QR - 1 -2 1 - 1 2 3 factorization of matrix A A = 4 3 V1 = V2: 4 V3 - 1 1 6 4 1 6 9 1 2 3 Q=. R = (Type exact answers, using radicals as needed.)
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