# Find the Eigenvalues [[0,0.1,0.9],[0.6,0,0.4],[0.9,0.1,0]] Set up the formula to find the characteristic equation .
Substitute the known values in the formula.
Subtract the eigenvalue times the identity matrix from the original matrix.
Multiply by each element of the matrix.
Simplify each element of the matrix .
Rearrange .
Rearrange .
Rearrange .
Rearrange .
Rearrange .
Rearrange .
Rearrange .
Rearrange .
Rearrange .
Add the corresponding elements of to each element of .
Simplify each element of the matrix .
Simplify .
Simplify .
Simplify .
Simplify .
Simplify .
Simplify .
Simplify .
Simplify .
Simplify .
The determinant of is .
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 .
Multiply by .
Multiply by .
Multiply by .
Apply the distributive property.
Multiply by by adding the exponents.
Move .
Multiply by .
Raise to the power of .
Use the power rule to combine exponents.
Multiply by .
The determinant of is .
The determinant of a matrix can be found using the formula .
Simplify the determinant.
Simplify each term.
Multiply by .
Multiply by .
Simplify by multiplying through.
Apply the distributive property.
Multiply.
Multiply by .
Multiply by .
The determinant of is .
The determinant of a matrix can be found using the formula .
Simplify the determinant.
Simplify each term.
Multiply by .
Move to the left of .
Simplify by multiplying through.
Apply the distributive property.
Multiply.
Multiply by .
Multiply by .
Can’t combine different size matrices.
The combined expressions are .
Factor out of .
Factor out of .
Factor out of .
Factor out of .
Factor out of .
Factor out of .
Set the characteristic polynomial equal to to find the eigenvalues .
Solve the equation for .
Simplify .
Apply the distributive property.
Simplify.
Multiply by .
Multiply by .
Multiply by .
Rewrite as .
Graph each side of the equation. The solution is the x-value of the point of intersection.
Find the Eigenvalues [[0,0.1,0.9],[0.6,0,0.4],[0.9,0.1,0]]

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