# Linear 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 .

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.

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

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

Simplify each term.

Apply the distributive property.

Move .

Simplify .

Use the power rule to combine exponents.

Add and .

Multiply by .

Simplify .

Multiply by .

Multiply by .

Multiply by .