Linear Algebra Examples

Solve Using an Inverse Matrix y=36-9x , 3x+y/3=12
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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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Cancel the common factor of .
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Factor out of .
Cancel the common factor.
Rewrite the expression.
Multiply by .
Subtract from .
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