Precalculus Examples

Solve Using an Inverse Matrix
,
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 by .
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.
Simplify each element in the matrix.
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Rearrange .
Rearrange .
Rearrange .
Rearrange .
Step 3
Left multiply both sides of the matrix equation by the inverse matrix.
Step 4
Any matrix multiplied by its inverse is equal to all the time. .
Step 5
Simplify the right side of the equation.
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Multiply each row in the first matrix by each column in the second matrix.
Simplify each element of the matrix by multiplying out all the expressions.
Step 6
Simplify the left and right side.
Step 7
Find the solution.
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