# Linear Algebra Examples

Solve Using a Matrix with Cramer's Rule
,
Represent the system of equations in matrix format.
The determinant of is .
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 to get .
Multiply by to get .
Add and to get .
The determinant of is .
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 to get .
Multiply by to get .
Add and to get .
The determinant of is .
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 to get .
Multiply by to get .
Add and to get .
Remove the extra parentheses from the expression .
Remove the parentheses from the numerator.
Remove the parentheses from the denominator.
Remove the extra parentheses from the expression .
Remove the parentheses from the numerator.
Remove the parentheses from the denominator.
The solution to the system of equations using Cramer's Rule.