Algebra Examples

Find the Inverse of the Matrix
The inverse of a matrix can be found using the formula where is the determinant of .
If then
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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Multiply by to get .
Multiply by to get .
Subtract from to get .
Substitute the known values into the formula for the inverse of a matrix.
Simplify each element of the matrix .
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Simplify element by multiplying to get .
Simplify element by multiplying to get .
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 .
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