Write the system as a matrix equation and solve using inverses.

Question

2x1 + x2 = 2
5x1 + 3x2 = 13

 

Write the system as a matrix equation and solve using inverses.

 

Answer 1

A = [ 2  1 ]

      [ 5  3 ]

 

C = [ 2 ]

      [13 ]

 

X = [x₁ ]

      [x₂ ]

 

Matrix equation: AX = C so therefore X = A^-1C.

 

Now all you have to do is to calculate the inverse of square matrix A, and multiply it by the columnar matrix C.

 

The procedure for inverting a square 2-D matrix is easy if done on paper, and is even easier if you let a graphing calculator do it.