Find the Eigenvalues [[0,0.1,0.9],[0.6,0,0.4],[0.9,0.1,0]]

Math
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.
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Multiply by each element of the matrix.
Simplify each element of the matrix .
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Rearrange .
Rearrange .
Rearrange .
Rearrange .
Rearrange .
Rearrange .
Rearrange .
Rearrange .
Rearrange .
Add the corresponding elements of to each element of .
Simplify each element of the matrix .
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Simplify .
Simplify .
Simplify .
Simplify .
Simplify .
Simplify .
Simplify .
Simplify .
Simplify .
The determinant of is .
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Set up the determinant by breaking it into smaller components.
The determinant of is .
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The determinant of a matrix can be found using the formula .
Simplify the determinant.
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Simplify each term.
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Multiply by .
Multiply by .
Multiply by .
Multiply by .
Apply the distributive property.
Multiply by by adding the exponents.
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Move .
Multiply by .
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Raise to the power of .
Use the power rule to combine exponents.
Add and .
Multiply by .
The determinant of is .
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The determinant of a matrix can be found using the formula .
Simplify the determinant.
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Simplify each term.
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Multiply by .
Multiply by .
Simplify by multiplying through.
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Apply the distributive property.
Multiply.
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Multiply by .
Multiply by .
The determinant of is .
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The determinant of a matrix can be found using the formula .
Simplify the determinant.
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Simplify each term.
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Multiply by .
Move to the left of .
Simplify by multiplying through.
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Apply the distributive property.
Multiply.
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Multiply by .
Multiply by .
Add and .
Add and .
Add and .
Can’t combine different size matrices.
The combined expressions are .
Factor out of .
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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 .
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Simplify .
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Apply the distributive property.
Simplify.
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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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