# 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.
Multiply by each element of the matrix.
Simplify each element of the matrix .
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 .
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.
The determinant of is .
These are both valid notations for the determinant of a matrix.
The determinant of a matrix can be found using the formula .
Simplify each term.
Apply the distributive property.
Move .
Use the power rule to combine exponents.
Multiply by to get .
Simplify .
Multiply by to get .
Multiply by to get .
Multiply by to get .

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