Linear Algebra Examples

Solve Using an Inverse Matrix 1/3y-2/3x=1 , 10x-5y=-15
,
Step 1
Find the from the system of equations.
Step 2
Find the inverse of the coefficient matrix.
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The inverse of a matrix can be found using the formula where is the determinant of .
If then
Find the determinant of .
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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 .
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Multiply by .
Combine and .
Multiply by .
Combine and .
Move the negative in front of the fraction.
Combine fractions.
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Combine the numerators over the common denominator.
Simplify the expression.
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Subtract from .
Divide by .
Substitute the known values into the formula for the inverse of a matrix.
Simplify each element in the matrix.
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Rearrange .
Rearrange .
Multiply by each element of the matrix.
Rearrange .
Since the matrix is undefined, it cannot be solved.
Undefined