Linear Algebra Examples
, ,
Step 1
Subtract from both sides of the equation.
Subtract from both sides of the equation.
Step 2
Subtract from both sides of the equation.
Step 3
Subtract from both sides of the equation.
Step 4
Represent the system of equations in matrix format.
Step 5
Set up the determinant by breaking it into smaller components.
Find the determinant of .
The determinant of a matrix can be found using the formula .
Simplify the determinant.
Simplify each term.
Multiply by .
Multiply by .
Simplify the expression.
Subtract from .
Multiply by .
Find the determinant of .
The determinant of a matrix can be found using the formula .
Simplify the determinant.
Simplify each term.
Multiply by .
Multiply by .
Simplify the expression.
Add and .
Multiply by .
Since the matrix is multiplied by , the determinant is .
Subtract from .
Add and .
Step 6
Set up the determinant by breaking it into smaller components.
Find the determinant of .
The determinant of a matrix can be found using the formula .
Simplify the determinant.
Simplify each term.
Multiply by .
Multiply by .
Simplify the expression.
Subtract from .
Multiply by .
Find the determinant of .
The determinant of a matrix can be found using the formula .
Simplify the determinant.
Simplify each term.
Multiply by .
Multiply by .
Simplify the expression.
Add and .
Multiply by .
Since the matrix is multiplied by , the determinant is .
Add and .
Add and .
Step 7
Set up the determinant by breaking it into smaller components.
Find the determinant of .
The determinant of a matrix can be found using the formula .
Simplify the determinant.
Simplify each term.
Multiply by .
Multiply by .
Simplify the expression.
Add and .
Multiply by .
Find the determinant of .
The determinant of a matrix can be found using the formula .
Simplify the determinant.
Simplify each term.
Multiply by .
Multiply by .
Simplify the expression.
Add and .
Multiply by .
Since the matrix is multiplied by , the determinant is .
Add and .
Add and .
Step 8
Set up the determinant by breaking it into smaller components.
Find the determinant of .
The determinant of a matrix can be found using the formula .
Simplify the determinant.
Simplify each term.
Multiply by .
Multiply by .
Simplify the expression.
Subtract from .
Multiply by .
Find the determinant of .
The determinant of a matrix can be found using the formula .
Simplify the determinant.
Simplify each term.
Multiply by .
Multiply by .
Simplify the expression.
Add and .
Multiply by .
Since the matrix is multiplied by , the determinant is .
Add and .
Add and .
Step 9
Remove parentheses.
Divide by .
Step 10
Remove parentheses.
Divide by .
Step 11
Remove parentheses.
Divide by .
Step 12
The solution to the system of equations using Cramer's Rule.