# Algebra Examples

Step 1
Set up the formula to find the characteristic equation .
Step 2
Substitute the known values in the formula.
Step 3
Subtract the eigenvalue times the identity matrix from the original matrix.
Multiply by each element of the matrix.
Simplify each element in the matrix.
Rearrange .
Rearrange .
Rearrange .
Rearrange .
Rearrange .
Rearrange .
Rearrange .
Rearrange .
Rearrange .
Simplify each element of the matrix .
Simplify .
Simplify .
Simplify .
Simplify .
Simplify .
Simplify .
Simplify .
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.
Apply the distributive property.
Multiply by .
Rewrite using the commutative property of multiplication.
Simplify each term.
Multiply by by adding the exponents.
Move .
Multiply by .
Multiply by .
Multiply by .
Multiply by .
Expand by multiplying each term in the first expression by each term in the second expression.
Simplify terms.
Simplify each term.
Multiply by .
Multiply by .
Rewrite using the commutative property of multiplication.
Multiply by by adding the exponents.
Move .
Multiply by .
Multiply by .
Multiply by by adding the exponents.
Move .
Multiply by .
Raise to the power of .
Use the power rule to combine exponents.
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 by multiplying through.
Apply the distributive property.
Multiply.
Multiply by .
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 .
Apply the distributive property.
Multiply by .
Multiply .
Multiply by .
Multiply by .
Apply the distributive property.
Multiply by .
Move to the left of .
Simplify by multiplying through.
Subtract from .
Apply the distributive property.
Multiply.
Multiply by .
Multiply by .
Combine the opposite terms in .