Warm up

Find the inverse of

Solving Systems Using Inverse Matrices

Systems to Matrices

• A system of equations in standard form (Ax+By=C) can be written in matrix form [A][X]=[B]

Where A are the coefficients, X are the variables and B are the constants.

Example 1

• Write the following system in matrix form.

Answer

Example 2: you try

Answer

Now go the other way

• Given a Matrix, write the system of equations.

Answer

11x – y = 54x + 8y = -3

Recall….

1. A matrix multiplied by the identity results in the original matrix

2. A matrix multiplied by its inverse gives you the identity.

Now we will want to solve systems using matrices

This means solving for x and y.

To do this we will multiply both sides of the equation by the inverse matrix.

Why this works (proof)No need to write this down, this is for those who are curious….

Steps

1. Put all equations in standard form. 2. Write system of equations in matrix form [A]

[X]=[B]3. Find either by hand or using the calculator.4. Multiply 5. The result from step 3 is your solution matrix,

which equals [X].

Example

Solve this system using inverse matrices.

Solution –Step 1

• First rewrite the second equation in standard form.

Solution- Step 2

• Write in Matrix form

Solution – step 3

• Find inverse on the calculator

Solution- step 4

• Multiply (by hand or on calculator)

Solution – step 5

• Write answer in matrix from

You try: with three variables!

• c represents the price of a candy bar• d represents the price of a drink• p represents the price of popcorn• Find the price of all three items.

Answer

[𝑐𝑑𝑝 ]=[2.152.052.75]

Homework

• Worksheet – All problems

• http://teachers.henrico.k12.va.us/math/hcpsalgebra2/Documents/4-6/4_6HW.pdf