solve the system of equations using the matrix method

1) solve the system of equations using the matrix method

a)

3*x1 + x2 + 5*x3 = 20

-x1 + 4*x2 = 0

2*x1 + 3*x2 - x3 = 7

b)

x1 + 5*x2 + x3 = 28

7*x1 + 3*x2 + x3 = 54

2*x1 - 5*x2 +x3 =-31

c)

4*x1 + 2*x2 + x3 = 18

4*x2 - x3 = -2

2*x1 + 3*x2 = 6

d)

2*x1 + 3*x2 + x4 = 8

2*x1 + x2 + 4*x3 + 2*x4 = 19

4*x1 + 2*x2 +x3 - 13 = 0

4*x2 - x3 +3*x4 = 4

Answer 1

[Sarvesh Kale]

Hi Connor,

start by writing the equations in matrix format ,

a.)

A = [3 1 5 ;...
    -1 4 0 ; ...
    2 3 -1
    ];

b = [20;...
    0;...
    7];

x= A\b 

x = 3×1

3.2353 0.8088 1.8971

b.)

A = [1 5 1;...
    7 3 1;...
    2 -5 1];

b= [28;54;-31];

x = A\b 

x = 3×1

6.5172 6.5517 -11.2759

c.)

A = [4 2 1; 0 4 -1; 2 3 0];
b = [18;-2;6];
x= A\b % the A matrix is singular i.e the determinant is zero 

Warning: Matrix is singular to working precision.

x = 3×1

Inf -Inf -Inf

d.)

A = [2 3 0 1;2 1 4 2;4 2 1 0;0 4 -1 3];
b = [8;19;13;4];

x= A\b

x = 4×1

2 1 3 1

I hope this helps !

[Connor]

yes it does, thank you so much!