Find the Eigenvalues [[two , one],[three , two]]

Find the Eigenvalues [[2,1],[3,2]]
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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First, multiply by each element of the matrix.
Clarify 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 .
Clarify the determinant.
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Clarify each term.
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Expand using the FOIL Method.
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Use the distributive law.
Apply the distributive property.
Apply the distributive property.
Clarify and Add like terms.
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Simplify each term.
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Multiply by .
Multiply by .
Multiply by .
Initially, multiply by .
Multiply by .
Multiply by .
Subtract from .
Multiply by .
Subtract from .
Set the characteristic polynomial equal to to find the eigenvalues .
Find solution to the equation for .
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Apply the quadratic formula to solve the equation.
Substitute the values , , and into the quadratic formula and solve for .
Simplify.
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Clarify the numerator.
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Raise to the power of .
First, multiply by .
Multiply by .
Subtract from .
Should be rewritten as .
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Factor out of .
Rewrite as .
Withdraw terms from under the radical.
Multiply by .
Simplify .
Clarify 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 .
Subtract from .
Rewrite as .
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Factor out of .
Rewrite as .
Pull terms out from under the radical.
Multiply by .
Simplify .
Change the to .
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 .
Subtract from .
Rewrite as .
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Factor out of .
Rewrite as .
Pull terms out from under the radical.
Multiply by .
Simplify .
Change the to .
The combination of 2 solutions is the answer.
The result can be displayed in a variety of ways.
Exact Form:
Decimal Form:
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