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
Subtract the eigenvalue times the identity matrix from the original matrix.
Tap for more steps...
Multiply by each element of the matrix.
Simplify each element in the matrix.
Tap for more steps...
Rearrange .
Rearrange .
Rearrange .
Rearrange .
Rearrange .
Rearrange .
Rearrange .
Rearrange .
Rearrange .
Add the corresponding elements.
Simplify each element of the matrix .
Tap for more steps...
Simplify .
Simplify .
Simplify .
Simplify .
Simplify .
Simplify .
Simplify .
Step 4
Find the determinant of .
Tap for more steps...
Set up the determinant by breaking it into smaller components.
Find the determinant of .
Tap for more steps...
The determinant of a matrix can be found using the formula .
Simplify the determinant.
Tap for more steps...
Simplify each term.
Tap for more steps...
Apply the distributive property.
Multiply by .
Rewrite using the commutative property of multiplication.
Simplify each term.
Tap for more steps...
Multiply by by adding the exponents.
Tap for more steps...
Move .
Multiply by .
Multiply by .
Multiply by .
Multiply by .
Expand by multiplying each term in the first expression by each term in the second expression.
Simplify terms.
Tap for more steps...
Simplify each term.
Tap for more steps...
Multiply by .
Multiply by .
Rewrite using the commutative property of multiplication.
Multiply by by adding the exponents.
Tap for more steps...
Move .
Multiply by .
Multiply by .
Multiply by by adding the exponents.
Tap for more steps...
Move .
Multiply by .
Tap for more steps...
Raise to the power of .
Use the power rule to combine exponents.
Add and .
Multiply by .
Simplify by adding terms.
Tap for more steps...
Add and .
Add and .
Find the determinant of .
Tap for more steps...
The determinant of a matrix can be found using the formula .
Simplify the determinant.
Tap for more steps...
Simplify each term.
Tap for more steps...
Multiply by .
Multiply by .
Simplify by multiplying through.
Tap for more steps...
Apply the distributive property.
Multiply.
Tap for more steps...
Multiply by .
Multiply by .
Find the determinant of .
Tap for more steps...
The determinant of a matrix can be found using the formula .
Simplify the determinant.
Tap for more steps...
Simplify each term.
Tap for more steps...
Multiply by .
Apply the distributive property.
Multiply by .
Multiply .
Tap for more steps...
Multiply by .
Multiply by .
Apply the distributive property.
Multiply by .
Move to the left of .
Simplify by multiplying through.
Tap for more steps...
Subtract from .
Apply the distributive property.
Multiply.
Tap for more steps...
Multiply by .
Multiply by .
Add and .
Combine the opposite terms in .
Tap for more steps...
Add and .
Add and .
Add and .
Add and .
Factor the characteristic polynomial.
Tap for more steps...
Factor out of .
Tap for more steps...
Factor out of .
Factor out of .
Factor out of .
Factor out of .
Factor out of .
Reorder terms.
Enter YOUR Problem
Mathway requires javascript and a modern browser.
Cookies & Privacy
This website uses cookies to ensure you get the best experience on our website.
More Information