Converting Linear Equations to Matrix Form

Hello,

I am trying to convert the following equations into matrix form.

Thanks.

[Mohammadali Mozafarian]

Hi Connor,

You wouldn't need to ask the question here. If you review your lecture notes, you will find the answer there!

Sepehr

Answer 1

[Bjorn Gustavsson]

Is k some sort of propagation (time? space?) index and you want to convert these equations into a matrix-format, or are these actually some scalilng-factors?

In case 1:

C = [C11 0 0 0;C21 C22 0 0;0 C32 C33 0;0 0 C43 C44];
ad = [a;d;0;0];
x_next = C*x_curr + ad;

In case 2:

C = [C11*k-(k+1) 0 0 0;C21*k C22*k-(k+1) 0 0;0 C32*k C33*k-(k+1) 0;0 0 C43*k C44*k-(k+1)];
ad = -[a;d;0;0];
x = C\ad;

Think I got this right, not checked or tested.

HTH

[Connor Wright]

Honestly I have not been given any context what k is, just know I need to convert the equations into matrix form.

[Bjorn Gustavsson]

Before you continue coding you'd better get the context! You need to know if you're implementing a stepper that intends to solve some sort of difference equation (or ordinary differential equations), or if you're supposed to get a solution for a single system of equations. Before you code something you have to know what problem you're supposed to solve.

Regardless of that I've given you solutions to the two plausible variants I could guess, from there it's your job to get the information you need to understand which one to chose.

Answer 2

[Hernia Baby]

You need to convert following form.

X(i+1) = C*X(i) + a(i)

Xo = [0 0 0 0]';
X(:,1) = Xo;

C11 = 1;
C21 = 2; C22 = 3;
C32 = 4; C33 = 5;
C43 = 6; C44 = 7;

C = [C11 0 0 0; C21 C22 0 0; 0 C32 C33 0; 0 0 C43 C44]

step_num = 5;
a = zeros(4,step_num);
a(1:2,:) = randn(2, step_num);

i = 1;
while i <= step_num
    X = C*X + a(:,i);
    i = i + 1;
    X
end