# 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 to get .

Simplify element by multiplying to get .

Simplify element by multiplying to get .

Simplify element by multiplying to get .

Simplify element by multiplying to get .

Simplify element by multiplying to get .

Simplify element by multiplying to get .

Simplify element by multiplying to get .

Simplify element by multiplying to get .

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.

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.

Multiply by to get .

Apply the distributive property.

Simplify .

Multiply by to get .

Multiply by to get .

Multiply by to get .

Simplify the expression.

Remove unnecessary parentheses.

Add and to get .

Since the matrix is multiplied by , the determinant is .

The determinant of is .

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

Simplify the determinant.

Simplify terms.

Simplify each term.

Expand using the FOIL Method.

Apply the distributive property.

Apply the distributive property.

Apply the distributive property.

Remove parentheses.

Simplify and combine like terms.

Simplify each term.

Move .

Use the power rule to combine exponents.

Add and to get .

Simplify .

Multiply by to get .

Multiply by to get .

Multiply by to get .

Multiply by to get .

Multiply by to get .

Subtract from to get .

Multiply by to get .

Subtract from to get .

Expand by multiplying each term in the first expression by each term in the second expression.

Simplify terms.

Remove unnecessary parentheses.

Simplify each term.

Move .

Use the power rule to combine exponents.

Add and to get .

Move .

Use the power rule to combine exponents.

Add and to get .

Multiply by to get .

Multiply by to get .

Multiply by to get .

Multiply by to get .

Multiply by to get .

Simplify by adding terms.

Add and to get .

Add and to get .

Add and to get .

Add and to get .

Subtract from to get .

Set the characteristic polynomial equal to to find the eigenvalues .

The roots of this equation could not be found algebraically, so the roots were determined numerically.