Linear Algebra Examples

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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Simplify element by multiplying to get .
Simplify element by multiplying to get .
Simplify element by multiplying to get .
Simplify element by multiplying to get .
Simplify element by multiplying to get .
Simplify element by multiplying to get .
Simplify element by multiplying to get .
Simplify element by multiplying to get .
Simplify element by multiplying to get .
Combine the similar matrices with each others.
Simplify each element of the matrix .
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Combine the same size matrices and by adding the corresponding elements of each.
Simplify element of the matrix.
Simplify element of the matrix.
Simplify element of the matrix.
Simplify element of the matrix.
Simplify element of the matrix.
Simplify element of the matrix.
Simplify element of the matrix.
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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Apply the distributive property.
Move .
Use the power rule to combine exponents.
Add and to get .
Multiply by to get .
Simplify .
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Multiply by to get .
Multiply by to get .
Multiply by to get .
Expand by multiplying each term in the first expression by each term in the second expression.
Simplify terms.
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Remove unnecessary parentheses.
Simplify each term.
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Move .
Use the power rule to combine exponents.
Add and to get .
Move .
Use the power rule to combine exponents.
Add and to get .
Multiply by to get .
Multiply by to get .
Multiply by to get .
Multiply by to get .
Simplify by adding terms.
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Add and to get .
Subtract from to get .
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 to get .
Multiply by to get .
Simplify by multiplying through.
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Apply the distributive property.
Multiply.
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Multiply by to get .
Multiply by to get .
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 to get .
Apply the distributive property.
Simplify .
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Multiply by to get .
Multiply by to get .
Multiply by to get .
Apply the distributive property.
Move to the left of the expression .
Multiply by to get .
Multiply by to get .
Simplify by multiplying through.
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Remove unnecessary parentheses.
Subtract from to get .
Apply the distributive property.
Multiply.
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Multiply by to get .
Multiply by to get .
Add and to get .
Add and to get .
Simplify by adding numbers.
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Add and to get .
Add and to get .
Add and to get .
Factor out of .
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Factor out of .
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Factor out of .
Move .
Multiply by to get .
Factor out of .
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Factor out of .
Move .
Multiply by to get .
Reorder and .
Factor out of .
Factor out of .
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