The matrix equation (Ax = b) [3 -2 X1 1 X2 1 1 has no solution. We wish to find the best approximate solution to this system. 1. Write the system of equations used to find the best approximation (i.e., write the system corresponding to the "normal equations").

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter9: Systems Of Equations And Inequalities
Section9.7: The Inverse Of A Matrix
Problem 30E
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The matrix equation (Ax = b)
Г3 —2]
X1
1
=
X2
1
has no solution. We wish to find the best approximate solution to this system.
1. Write the system of equations used to find the best approximation (i.e., write the system corresponding
to the "normal equations").
2. The solution to the system of normal equations is
X =
3. The vector in the column space of A nearest to the vector b is
Transcribed Image Text:The matrix equation (Ax = b) Г3 —2] X1 1 = X2 1 has no solution. We wish to find the best approximate solution to this system. 1. Write the system of equations used to find the best approximation (i.e., write the system corresponding to the "normal equations"). 2. The solution to the system of normal equations is X = 3. The vector in the column space of A nearest to the vector b is
4. The "error vector" (i.e., the difference between b and the nearest vector) is
5. The magnitude of the error is
00
Transcribed Image Text:4. The "error vector" (i.e., the difference between b and the nearest vector) is 5. The magnitude of the error is 00
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