# Algebra Examples

Solve Using an Inverse Matrix
,
Step 1
Find the from the system of equations.
Step 2
Find the inverse of the coefficient matrix.
The inverse of a matrix can be found using the formula where is the determinant of .
If then
Find the determinant of .
These are both valid notations for the determinant of a matrix.
The determinant of a matrix can be found using the formula .
Simplify the determinant.
Simplify each term.
Multiply by .
Multiply by .
Subtract from .
Substitute the known values into the formula for the inverse of a matrix.
Simplify each element in the matrix.
Rearrange .
Rearrange .
Multiply by each element of the matrix.
Simplify each element in the matrix.
Rearrange .
Rearrange .
Rearrange .
Rearrange .
Step 3
Left multiply both sides of the matrix equation by the inverse matrix.
Step 4
Any matrix multiplied by its inverse is equal to all the time. .
Step 5
Simplify the right side of the equation.
Multiply each row in the first matrix by each column in the second matrix.
Simplify each element of the matrix by multiplying out all the expressions.
Step 6
Simplify the left and right side.
Step 7
Find the solution.