PLEASE USE MATLAB TO ANSWER ALL QUESTIONS AND SHOW CODE USED! THANKS! 6. Conside

Question

PLEASE USE MATLAB TO ANSWER ALL QUESTIONS AND SHOW CODE USED! THANKS!

6. Consider the inconsistent linear system -i+2+103-19 (a) Enter the coefficient matrix A and the vector b into MATLAB for which this system is Ax = b. Use the command MCA b to enter the augmented matrix of the system, and then do a (b) We shall find a least-squares solution instead. As in the guide, enter the augmented matrix N of c) Compute the distance from Aw to b. This is the quantity that the least-squares solution mini (d) Choose a vector v whose entries are close to those of w, but different. Verify that the distance command to verify that the system is inconsistent the normal equations ATAx-Ab. Use rref to find the least-squares solution w. mizes from Av to b is larger than the quantity from the previous part.

Explanation / Answer

Matlab Code:

clc
clear all
close all

A = [ 1 3 5 ; 1 2 -1 ; 0 1 4; -1 1 10; 3 7 8 ]
B = [-2;0;-5;-19;6]

M = [A B]
Rank_M = rank (M)

X = AB
C = pinv(A)*B

B1 = A*C

Output:

A =

1 3 5
1 2 -1
0 1 4
-1 1 10
3 7 8

B =

-2
0
-5
-19
6

M =

1 3 5 -2
1 2 -1 0
0 1 4 -5
-1 1 10 -19
3 7 8 6

RankM =

4

X =

23.4708
-10.9708
1.5345

C =

23.4708
-10.9708
1.5345

B1 =

-1.7692
-0.0053
-4.8329
-19.0968
5.8926

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