# Linear Algebra Examples

Step 1

Set up the formula to find the characteristic equation .

Step 2

Substitute the known values in the formula.

Step 3

Multiply by each element of the matrix.

Simplify each element in the matrix.

Rearrange .

Rearrange .

Rearrange .

Rearrange .

Add the corresponding elements.

Simplify each element of the matrix .

Simplify .

Simplify .

Simplify .

Step 4

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.

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 .

Step 5

Reorder the polynomial.