Introduction to Linear Systems
Systems of Linear Equations
The foundation of linear algebra
A system of linear equations has variables appearing only to the first power. We can represent any such system as a matrix equation Ax = b.
Matrix Form
Ax = b
A is the coefficient matrix, x is the variable vector, b is the constant vector
Converting to Matrix Form
Easy
Write as a matrix equation: 2x + 3y = 7, x - y = 1
1
Identify components
A = [2 3; 1 -1], x = [x; y], b = [7; 1]
2
Write matrix equation
[2 3; 1 -1][x; y] = [7; 1]
Answer:
[2 3; 1 -1][x; y] = [7; 1]