# Linear Algebra Examples

Step 1
Set up the determinant by breaking it into smaller components.
Step 2
Find the determinant of .
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.
Subtract from .
Multiply by .
Since the matrix is multiplied by , the determinant is .
Subtract from .
Step 3
Since the matrix is multiplied by , the determinant is .
Step 4
Find the determinant of .
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 .
Since the matrix is multiplied by , the determinant is .
Multiply by .
Step 5
Find the determinant of .
Set up the determinant by breaking it into smaller components.
Since the matrix is multiplied by , the determinant is .
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 .
Subtract from .