Finite Math Examples

Find the Inverse [[1/5,1/2],[1/3,0]]
Step 1
The inverse of a matrix can be found using the formula where is the determinant.
Step 2
Find the determinant.
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Step 2.1
The determinant of a matrix can be found using the formula .
Step 2.2
Simplify the determinant.
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Step 2.2.1
Simplify each term.
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Step 2.2.1.1
Multiply by .
Step 2.2.1.2
Multiply .
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Step 2.2.1.2.1
Multiply by .
Step 2.2.1.2.2
Multiply by .
Step 2.2.2
Subtract from .
Step 3
Since the determinant is non-zero, the inverse exists.
Step 4
Substitute the known values into the formula for the inverse.
Step 5
Cancel the common factor of and .
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Step 5.1
Rewrite as .
Step 5.2
Move the negative in front of the fraction.
Step 6
Multiply the numerator by the reciprocal of the denominator.
Step 7
Multiply .
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Step 7.1
Multiply by .
Step 7.2
Multiply by .
Step 8
Multiply by each element of the matrix.
Step 9
Simplify each element in the matrix.
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Step 9.1
Multiply by .
Step 9.2
Cancel the common factor of .
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Step 9.2.1
Move the leading negative in into the numerator.
Step 9.2.2
Factor out of .
Step 9.2.3
Cancel the common factor.
Step 9.2.4
Rewrite the expression.
Step 9.3
Multiply by .
Step 9.4
Cancel the common factor of .
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Step 9.4.1
Move the leading negative in into the numerator.
Step 9.4.2
Factor out of .
Step 9.4.3
Cancel the common factor.
Step 9.4.4
Rewrite the expression.
Step 9.5
Multiply by .
Step 9.6
Combine and .
Step 9.7
Move the negative in front of the fraction.