In these lessons, we will how to solve Systems of Equations or Simultaneous Equations using Matrices.
First, we would look at how the inverse of a matrix can be used to solve a matrix equation.
Given the matrix equation AY = B, find the matrix Y.
If we multiply each side of the equation by A-1, we get
A-1A Y = A-1B
I Y = A -1B ( AA -1= I, where I is the identity matrix)
Y = A -1B ( IY = Y, any matrix multiply with the identity matrix will be unchanged)
Using matrices, calculate the values of x and y for the following simultaneous equations:
2x – 2y – 3 = 0
8 y = 7x + 2
Step 1: Write the equations in the form ax + by = c
2x – 2y – 3 = 0 ⇒ 2x – 2y = 3
8y = 7x + 2 ⇒ 7x – 8y = –2
Step 2: Write the equations in matrix form.
Step 3: Find the inverse of the 2 × 2 matrix.
Determinant = (2 × –8) – (–2 × 7) = – 2
Step 4: Multiply both sides of the matrix equations with the inverse
So, x = 14 and y = 12.5