Extract values from one matrix and with iteration solve the system of linear equations

Hello everyone!

Please, help me write a code for solving the system of linear equations in Matlab

If I have a column of coefficients A [A1;A2;A3] and the inverse matrix 3x3 B^(-1) and unknown column C [C1, C1, C1] (here all values are equal)

I have to find C1 value and plot the graph. Also A1 values can be extraacted from another matrix, so unknowns are A2, A3 and C1

A.'*B^(-1) = C

[Torsten]

A is 3x1, B^(-1) is 3x3, thus A*B^(-1) is not defined. Maybe you mean

A.'*B^(-1) = C

instead of

A*B^(-1)=C1

?

[Alina Abdikadyr]

yes

Answer 1

[Walter Roberson]

A = randi([-5 5], 5 ,3)

A = 5×3

0 -4 -5 5 3 -4 -1 -1 0 4 3 -5 5 4 -4

B = randi(9,3, 3)

B = 3×3

4 8 7 1 1 9 9 6 1

C = A/B

C = 5×3

-0.7494 -0.0098 0.3342 -0.0319 -0.4889 0.6241 -0.0663 0.0614 -0.0885 0.1057 -0.6904 0.4742 0.1646 -0.6339 0.5528

plot(C(:,1))

[Alina Abdikadyr]

Thank you for your answer! but A2 and A3 coefficients for me are unknown. So (A1, A2, A3)*B matrix = (C1,C1,C1). I should find A2, A3 and C1

Answer 2

[Torsten]

B = rand(3,3);
A1 = 4;

rhs = -A1*B(1,:).';
Mat = [-ones(3,1),B(2:3,:).'];
sol = Mat\rhs;
C1 = sol(1)

C1 = 9.4544

A2 = sol(2)

A2 = 80.7027

A3 = sol(3)

A3 = -250.8747

[A1 A2 A3]*B-[C1 C1 C1]

ans = 1×3

1.0e-14 * -0.3553 -0.3553 -0.7105

[Alina Abdikadyr]

Thank you very much! Can you please also help me, If I have different values of A1, so how the code would look like? (for each A1 I should calculate A2, A3, C1), at the end I'll have for example 5 values of A1, and A2 A3, C1 will be also 5

[Torsten]

Use a loop:

B = rand(3,3);
A1 = [4,pi,-80,329];

C1 = zeros(size(A1));
A2 = zeros(size(A1));
A3 = zeros(size(A1));
for i=1:numel(A1)
  rhs = -A1(i)*B(1,:).';
  Mat = [-ones(3,1),B(2:3,:).'];
  sol = Mat\rhs;
  C1(i) = sol(1);
  A2(i) = sol(2);
  A3(i) = sol(3);
  [A1(i) A2(i) A3(i)]*B-[C1(i) C1(i) C1(i)];
end

C1 = 1×4

-10.8402 0 0 0

A2 = 1×4

-19.4251 0 0 0

A3 = 1×4

-0.3832 0 0 0

ans = 1×3

1.0e-14 * -0.1776 -0.1776 0

C1 = 1×4

-10.8402 -8.5139 0 0

A2 = 1×4

-19.4251 -15.2565 0 0

A3 = 1×4

-0.3832 -0.3009 0 0

ans = 1×3

1.0e-14 * 0 -0.1776 -0.1776

C1 = 1×4

-10.8402 -8.5139 216.8035 0

A2 = 1×4

-19.4251 -15.2565 388.5023 0

A3 = 1×4

-0.3832 -0.3009 7.6631 0

ans = 1×3

1.0e-13 * -0.2842 -0.2842 0

C1 = 1×4

-10.8402 -8.5139 216.8035 -891.6043

A2 = 1×4

1.0e+03 * -0.0194 -0.0153 0.3885 -1.5977

A3 = 1×4

-0.3832 -0.3009 7.6631 -31.5146

ans = 1×3

1.0e-12 * 0 0 -0.1137

[Alina Abdikadyr]

Thank you!!!!!