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Linear Algebra With Applications
Found in: Page 247
Linear Algebra With Applications

Linear Algebra With Applications

Book edition 5th
Author(s) Otto Bretscher
Pages 442 pages
ISBN 9780321796974

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Short Answer

Find the least square x* of the system Ax=b where A=[123456789] and b=[100] .

The solution x=-7610+t1-21.

See the step by step solution

Step by Step Solution

Step1: Explanation of the solution

Consider the system as follows.

Ax=bwhere A=123456789 and b=100.

Consider the matrix A as follows.


Now, find ATA as follows.

ATA=123456789T123456789 =147258369123456789 =667890789310890108126ATA=667890789310890108126

The exact solution of the system is as follows.


After solving the matrix calculation as follows.


Then write the equation as follows.

x1-x3=-76x2+2x3=1x2+2x3=1 x3=t

Simplify further as follows.


Hence, the least square for the system ATAx=ATb is x=-7610+t1-21 .

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