consider the following system of 2 equations: 𝑥 + 𝑦 = 1 3𝑥 − 𝑦 = −1. write this system as a matrix equation and solve the system in matlab. in matlab

To write the given system of equations as a matrix equation, we can represent the coefficients of the variables using a matrix and represent the variables themselves using a column vector.

So, we have:

1 1 * 𝑥 = 1 3 -1 * 𝑦 = -1

Writing it in matrix form, we have:

⎡ 1 1 ⎤ ⎡𝑥⎤ ⎡ 1 ⎤ ⎣ 3 -1 ⎦ * ⎣𝑦⎦ = ⎣-1 ⎦

To solve the system in MATLAB, we can define the matrix A and column vector b as:

main.m
A = [1 1; 3 -1];
b = [1; -1];
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And then use the backslash operator to solve for x:

main.m
x = A \ b;
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This will give us the solution vector x, which contains the values of 𝑥 and 𝑦 that satisfy the system of equations.