Lesson: Solving a System of Three Equations Using a Matrix Inverse Mathematics

In this lesson, we will learn how to solve a system of three linear equations using the inverse of the matrix of coefficients.

Lesson Plan

Students will be able to

write a system of equations in matrix form,
solve a system of three equations using inverse matrices to find a unique solution,
solve word problems involving a system of three equations using an inverse matrix.

Q1:

Consider the system of equations

Express the system as a single matrix equation.

Work out the inverse of the coefficient matrix.

Multiply through by the inverse, on the left-hand side, to solve the matrix equation.

Q2:

Use matrices to solve the following system of equations:

Q3:

Use the inverse of a matrix to solve the system of linear equations , , and .