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The matrix equation (Ax = b) 2 1 1 x2 1 2 has no solution. We wish to find the best approximate solution to this system.

The matrix equation (Ax = b) 2 1 1 x2 1 2 has no solution. We wish to find the best approximate solution to this system.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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5. The magnitude of the error is
Transcribed Image Text:5. The magnitude of the error is
The matrix equation (Ax = b) 2 1 x1 1 %3D X2 1 2 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
Transcribed Image Text:The matrix equation (Ax = b) 2 1 x1 1 %3D X2 1 2 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
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