Linear Algebra Examples

Solve Using a Matrix with Cramer's Rule
, ,
Move to the left side of the equation because it contains a variable.
Move all terms containing variables to the left side of the equation.
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 .
Set up the determinant by breaking it into smaller components.
The determinant of is .
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 .
Simplify the expression.
Multiply by to get .
Since the matrix is multiplied by , the determinant is .
The determinant of is .
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 .
Subtract from to get .
Subtract from to get .
The determinant of is .
Set up the determinant by breaking it into smaller components.
The determinant of is .
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 .
Simplify the expression.
Multiply by to get .
Since the matrix is multiplied by , the determinant is .
The determinant of is .
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 .
Subtract from to get .
The determinant of is .
Set up the determinant by breaking it into smaller components.
The determinant of is .
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 .
Simplify the expression.
Multiply by to get .
Since the matrix is multiplied by , the determinant is .
The determinant of is .
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 .
Subtract from to get .
Subtract from to get .
The determinant of is .
Set up the determinant by breaking it into smaller components.
The determinant of is .
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 .
Simplify the expression.
Subtract from to get .
Multiply by to get .
The determinant of is .
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 .
Simplify the expression.
Multiply by to get .
The determinant of is .
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 .
Simplify the expression.
Multiply by to get .
Subtract from 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.
Find the value of by Cramer's Rule, which states that . In this case, .
Remove the extra parentheses from the expression .
Remove the parentheses from the numerator.
Remove the parentheses from the denominator.
Divide by to get .
The solution to the system of equations using Cramer's Rule.

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