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# Lab 7 Solutions

## Introduction

It appears that this lab does not have solutions or they are not yet posted.

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## Exercise 1

A = [1 -1;
3 5];
b = [5;1];

x = A\b
x =

3.2500
-1.7500



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## Exercise 2

A = [1 -1 3;
3 5 -1;
0 5 -3];
b = [5;1;-22];

x = A\b
x =

10.3846
-6.8462
-4.0769



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## Exercise 3

A = [1 -4 4;
-1 1 -2;
1 1 -1];
b = [0; 1; -2];

x = A\b
x =

-1.6000
-0.2000
0.2000



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## Exercise 4

x = [1,2,3];
y = [3,5,-1];

A = [x(:).^2 x(:) ones(3,1)];
b = y(:);

p = A\b
p =

-4.0000
14.0000
-7.0000



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## Exercise 5

z = ones(5,1);
A = spdiags([z -2*z z],-1:1,5,5);
b = ones(5,1);

A
full(A)

x = A\b
A =

(1,1)       -2
(2,1)        1
(1,2)        1
(2,2)       -2
(3,2)        1
(2,3)        1
(3,3)       -2
(4,3)        1
(3,4)        1
(4,4)       -2
(5,4)        1
(4,5)        1
(5,5)       -2

ans =

-2     1     0     0     0
1    -2     1     0     0
0     1    -2     1     0
0     0     1    -2     1
0     0     0     1    -2

x =

-2.5000
-4.0000
-4.5000
-4.0000
-2.5000



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## Exercise 6

(Left as homework exercise)

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## Exercise 7

(Left as homework exercise)

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## Get the code

Do you want to try the above code fragments on your own? Download the Matlab script that produces this page here. (lab_7_solns.m) Published with MATLAB® 8.5