# Algebra Examples

Set up the formula to find the characteristic equation .

Substitute the known values in the formula.

Multiply by each element of the matrix.

Simplify each element of the matrix .

Simplify element by multiplying .

Simplify element by multiplying .

Simplify element by multiplying .

Simplify element by multiplying .

Simplify element by multiplying .

Simplify element by multiplying .

Simplify element by multiplying .

Simplify element by multiplying .

Simplify element by multiplying .

Combine the similar matrices with each others.

Simplify each element of the matrix .

Combine the same size matrices and by adding the corresponding elements of each.

Simplify element of the matrix.

Simplify element of the matrix.

Simplify element of the matrix.

Simplify element of the matrix.

Simplify element of the matrix.

Simplify element of the matrix.

Simplify element of the matrix.

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.

Apply the distributive property.

Multiply by .

Multiply by .

Simplify each term.

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 by adding the exponents.

Move .

Multiply by .

Raise to the power of .

Use the power rule to combine exponents.

Add and .

Multiply by .

Multiply by .

Multiply by .

Multiply by .

Multiply by .

Simplify by adding terms.

Add and .

Subtract from .

The determinant of is .

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 .

The determinant of is .

The determinant of a matrix can be found using the formula .

Simplify the determinant.

Simplify each term.

Multiply by .

Apply the distributive property.

Multiply .

Multiply by .

Multiply by .

Multiply by .

Apply the distributive property.

Move to the left of .

Multiply by .

Simplify by multiplying through.

Subtract from .

Apply the distributive property.

Multiply.

Multiply by .

Multiply by .

Add and .

Add and .

Simplify by adding numbers.

Add and .

Add and .

Add and .

Factor out of .

Factor out of .

Factor out of .

Factor out of .

Factor out of .

Factor out of .