Describe all least-squares solutions of the equation Ax = b. 10 1 1 11 0 A = 1 0 1 3 b = 9 110 The general least-squares solutions of Ax = b for the given matrix A and vector b are all vectors of the form x =+ Xa with x, free. (Simplify your answers.)

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter4: Polynomial And Rational Functions
Section4.6: Variation
Problem 8E
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Describe all least-squares solutions of the equation Ax = b.
10 1
1
1 10
3
b =
A =
10 1
1 10
3
The general least-squares solutions of Ax = b for the given matrix A and vector b are all vectors of the form x=+ Xa, with x, free.
(Simplify your answers.)
Transcribed Image Text:Describe all least-squares solutions of the equation Ax = b. 10 1 1 1 10 3 b = A = 10 1 1 10 3 The general least-squares solutions of Ax = b for the given matrix A and vector b are all vectors of the form x=+ Xa, with x, free. (Simplify your answers.)
Find a least-squares solution of Ax = b by (a) constructing the normal equations for x and (b) solving for x.
- 1
4
4
A =
2 - 3
b =
2
- 1
(a) Construct the normal equations for x.
X1
(Simplify your answers.)
X2
Transcribed Image Text:Find a least-squares solution of Ax = b by (a) constructing the normal equations for x and (b) solving for x. - 1 4 4 A = 2 - 3 b = 2 - 1 (a) Construct the normal equations for x. X1 (Simplify your answers.) X2
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