In these lessons, we will how to solve Systems of Equations or Simultaneous Equations using Matrices.
Solving Systems of Equations or Simultaneous Equations using algebra
More Algebra Lessons
Matrices and Inverse Matrices
Simultaneous equations or system of equations of the form ax + by = h
and cx + dy
can be solved using algebra.
Simultaneous equations can also be solved 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)
Matrices & Systems of Equations
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
The following video shows how matrices can be used to solve a system of equations.
Using the inverse of a matrix to solve a system of equations.
Using a Matrix Equation to Solve a System of Equations
This video shows how to solve a system of equations by using a matrix equation.
A 2 x 2 example and a 3 x 3 example are given.
The graphing calculator is integrated into the lesson.
Solving Simultaneous Equations Using Matrices.
Step by step solution.
Simultaneous Equations - Matrix Method.
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