Linear Algebra Examples

The matrix equation can be written as a set of equations.
Solve for in the first equation.
Replace all occurrences of with the solution found by solving the last equation for . In this case, the value substituted is .
Replace all occurrences of with the solution found by solving the last equation for . In this case, the value substituted is .
Solve for in the second equation.
Replace all occurrences of with the solution found by solving the last equation for . In this case, the value substituted is .
Replace all occurrences of with the solution found by solving the last equation for . In this case, the value substituted is .
Solve for in the third equation.
Replace all occurrences of with the solution found by solving the last equation for . In this case, the value substituted is .
Replace all occurrences of with the solution found by solving the last equation for . In this case, the value substituted is .
Simplify.
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Simplify the right side.
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Simplify the numerator.
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Simplify .
To write as a fraction with a common denominator, multiply by .
Write each expression with a common denominator of , by multiplying each by an appropriate factor of .
Combine the numerators over the common denominator.
Simplify the numerator.
Multiply the numerator by the reciprocal of the denominator.
Cancel the common factor of .
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Factor out the greatest common factor .
Cancel the common factor.
Rewrite the expression.
Multiply and .
Simplify the right side.
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Simplify each term.
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Simplify the numerator.
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Write as a fraction with denominator .
Multiply and .
Multiply the numerator by the reciprocal of the denominator.
Multiply by .
Simplify .
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Multiply and .
Multiply by .
To write as a fraction with a common denominator, multiply by .
Write each expression with a common denominator of , by multiplying each by an appropriate factor of .
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Combine.
Multiply by .
Combine the numerators over the common denominator.
Simplify the numerator.
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Multiply by .
Multiply by .
Add and .
Reduce the expression by cancelling the common factors.
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Factor out of .
Cancel the common factors.
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Factor out of .
Cancel the common factor.
Rewrite the expression.
List the solutions to the system of equations.
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