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

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 .
Add the corresponding elements of to each element of .
Simplify each element of the matrix .
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Simplify .
Simplify .
The determinant of is .
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These are both valid notations for the determinant of a matrix.
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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Expand using the FOIL Method.
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Apply the distributive property.
Apply the distributive property.
Apply the distributive property.
Simplify and combine like terms.
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Simplify each term.
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Multiply by .
Multiply by .
Multiply by .
Multiply by .
Multiply by .
Multiply by .
Subtract from .
Multiply by .
Subtract from .
Set the characteristic polynomial equal to to find the eigenvalues .
Solve the equation for .
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Use the quadratic formula to find the solutions.
Substitute the values , , and into the quadratic formula and solve for .
Simplify.
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Simplify the numerator.
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Raise to the power of .
Multiply by .
Multiply by .
Add and .
Rewrite as .
Pull terms out from under the radical, assuming positive real numbers.
Multiply by .
Simplify .
Simplify the expression to solve for the portion of the .
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Simplify the numerator.
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Raise to the power of .
Multiply by .
Multiply by .
Add and .
Rewrite as .
Pull terms out from under the radical, assuming positive real numbers.
Multiply by .
Simplify .
Change the to .
Add and .
Simplify the expression to solve for the portion of the .
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Simplify the numerator.
Tap for more steps…
Raise to the power of .
Multiply by .
Multiply by .
Add and .
Rewrite as .
Pull terms out from under the radical, assuming positive real numbers.
Multiply by .
Simplify .
Change the to .
Subtract from .
The final answer is the combination of both solutions.
Find the Eigenvalues [[0.1,0.9],[0.4,0.6]]

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