In Matlab Consider this series of linear equations: 3x1 +4x2 +2x3 x4 +x5 +7x6 +x

Question

In Matlab Consider this series of linear equations: 3x1 +4x2 +2x3 x4 +x5 +7x6 +x7 = 42 2x1 2x2 +3x3 4x4 +5x5 +2x6 +8x7 = 32 x1 +2x2 +3x3 +x4 +2x5 +4x6 +6x7 = 12 5x1 +10x2 +4x3 +3x4 +9x5 2x6 +x7 = 5 3x1 +2x2 2x3 4x4 5x5 6x6 +7x7 = 10 2x1 +9x2 +x3 +3x4 3x5 +5x6 +x7 = 18 x1 2x2 8x3 +4x4 +2x5 +4x6 +5x7 = 17 If you use the matrix inverse technique to solve the above equations, type the matrices(and/or vectors) you need to use, and the command(s) to solve the equations. If you would use the “matrix left division” technique to solve the equations. Type the command(s).

Explanation / Answer

The given system of equations is :

3x1 +   4x2 +   2x3    x4 +   x5 +   7x6 +   x7       = 42       [1]
2x1    2x2 +   3x3    4x4 +   5x5 +   2x6 +   8x7       = 32       [2]
x1    +   2x2 +   3x3 +   x4 +   2x5 +   4x6 +   6x7    = 12        [3]
5x1 +   10x2 +   4x3 +   3x4 +   9x5    2x6 +   x7        = 5        [4]
3x1 +   2x2    2x3    4x4    5x5    6x6 +   7x7    = 10        [5]
2x1 +   9x2 +   x3 +   3x4    3x5 +   5x6 +   x7        = 18       [6]
x1    2x2    8x3 +   4x4 +   2x5 +   4x6 +   5x7    = 17        [7]

which in MATRIX for AX=b can be written as :

A=
   3 4 2 -1 1 7 1
2 -2 3 -4 5 2 8
1 2 3 1 2 4 6
5 10 4 3 9 -2 1
3 2 -2 -4 -5 -6 7
-2 9 1 3 -3 5 1
1 -2 -8 4 2 4 5
     
and b =

42
32
12
-5
10
18
17
  
The solution using MATLAB can thus be obtained using the following code:

clear all
clc
%%

A=[3,4,2,-1,1,7,1;2,-2,3,-4,5,2,8;1,2,3,1,2,4,6;5,10,4,3,9,-2,1;...
3,2,-2,-4,-5,-6,7;-2,9,1,3,-3,5,1;1,-2,-8,4,2,4,5];

b=[42;32;12;-5;10;18;17];

X=A

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