# Linear Algebra Examples

Solve Using a Matrix with Cramer's Rule
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Move to the left side of the equation because it contains a variable.
Move to the left side of the equation because it contains a variable.
Move to the right side of the equation because it does not contain a variable.
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 .
Multiply by .
Subtract from .
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 .
Multiply by .
Subtract from .
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 .
Multiply by .
Subtract from .
Find the value of by Cramer's Rule, which states that . In this case, .
Remove the parentheses from the numerator.
Move the negative in front of the fraction.
Find the value of by Cramer's Rule, which states that . In this case, .
Remove the parentheses from the numerator.
Move the negative in front of the fraction.
The solution to the system of equations using Cramer's Rule.