# 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 .

Rearrange .

Rearrange .

Rearrange .

Rearrange .

Add the corresponding elements of to each element of .

Simplify each element of the matrix .

Simplify .

Simplify .

These are both valid notations for the determinant of a matrix.

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

Simplify the determinant.

Simplify each term.

Expand using the FOIL Method.

Apply the distributive property.

Apply the distributive property.

Apply the distributive property.

Simplify and combine like terms.

Simplify each term.

Multiply by .

Multiply by .

Multiply by .

Multiply by .

Multiply by .

Multiply by .

Subtract from .

Multiply by .

Subtract from .