Linear Algebra Examples

Step 1
The matrix equation can be written as a set of equations.
Step 2
Solve for in .
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Step 2.1
Rewrite the equation as .
Step 2.2
Move all terms not containing to the right side of the equation.
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Step 2.2.1
Subtract from both sides of the equation.
Step 2.2.2
Subtract from both sides of the equation.
Step 3
Replace all occurrences of with in each equation.
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Step 3.1
Replace all occurrences of in with .
Step 3.2
Simplify the right side.
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Step 3.2.1
Simplify .
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Step 3.2.1.1
Simplify each term.
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Step 3.2.1.1.1
Apply the distributive property.
Step 3.2.1.1.2
Simplify.
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Step 3.2.1.1.2.1
Multiply by .
Step 3.2.1.1.2.2
Multiply by .
Step 3.2.1.1.2.3
Multiply by .
Step 3.2.1.2
Simplify by adding terms.
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Step 3.2.1.2.1
Add and .
Step 3.2.1.2.2
Add and .
Step 3.3
Replace all occurrences of in with .
Step 3.4
Simplify the right side.
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Step 3.4.1
Simplify .
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Step 3.4.1.1
Simplify each term.
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Step 3.4.1.1.1
Apply the distributive property.
Step 3.4.1.1.2
Simplify.
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Step 3.4.1.1.2.1
Multiply by .
Step 3.4.1.1.2.2
Multiply by .
Step 3.4.1.1.2.3
Multiply by .
Step 3.4.1.2
Simplify by adding terms.
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Step 3.4.1.2.1
Add and .
Step 3.4.1.2.2
Add and .
Step 4
Solve for in .
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Step 4.1
Rewrite the equation as .
Step 4.2
Move all terms not containing to the right side of the equation.
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Step 4.2.1
Subtract from both sides of the equation.
Step 4.2.2
Add to both sides of the equation.
Step 4.2.3
Add and .
Step 5
Replace all occurrences of with in each equation.
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Step 5.1
Replace all occurrences of in with .
Step 5.2
Simplify the right side.
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Step 5.2.1
Simplify .
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Step 5.2.1.1
Simplify each term.
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Step 5.2.1.1.1
Apply the distributive property.
Step 5.2.1.1.2
Multiply by .
Step 5.2.1.1.3
Multiply by .
Step 5.2.1.2
Simplify by adding terms.
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Step 5.2.1.2.1
Subtract from .
Step 5.2.1.2.2
Subtract from .
Step 5.3
Replace all occurrences of in with .
Step 5.4
Simplify the right side.
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Step 5.4.1
Simplify .
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Step 5.4.1.1
Simplify each term.
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Step 5.4.1.1.1
Apply the distributive property.
Step 5.4.1.1.2
Multiply by .
Step 5.4.1.1.3
Multiply by .
Step 5.4.1.2
Simplify by adding terms.
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Step 5.4.1.2.1
Subtract from .
Step 5.4.1.2.2
Add and .
Step 6
Solve for in .
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Step 6.1
Rewrite the equation as .
Step 6.2
Move all terms not containing to the right side of the equation.
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Step 6.2.1
Subtract from both sides of the equation.
Step 6.2.2
Subtract from .
Step 6.3
Divide each term in by and simplify.
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Step 6.3.1
Divide each term in by .
Step 6.3.2
Simplify the left side.
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Step 6.3.2.1
Cancel the common factor of .
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Step 6.3.2.1.1
Cancel the common factor.
Step 6.3.2.1.2
Divide by .
Step 6.3.3
Simplify the right side.
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Step 6.3.3.1
Cancel the common factor of and .
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Step 6.3.3.1.1
Factor out of .
Step 6.3.3.1.2
Cancel the common factors.
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Step 6.3.3.1.2.1
Factor out of .
Step 6.3.3.1.2.2
Cancel the common factor.
Step 6.3.3.1.2.3
Rewrite the expression.
Step 7
Replace all occurrences of with in each equation.
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Step 7.1
Replace all occurrences of in with .
Step 7.2
Simplify the right side.
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Step 7.2.1
Simplify .
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Step 7.2.1.1
Multiply .
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Step 7.2.1.1.1
Combine and .
Step 7.2.1.1.2
Multiply by .
Step 7.2.1.2
To write as a fraction with a common denominator, multiply by .
Step 7.2.1.3
Combine and .
Step 7.2.1.4
Combine the numerators over the common denominator.
Step 7.2.1.5
Simplify the numerator.
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Step 7.2.1.5.1
Multiply by .
Step 7.2.1.5.2
Subtract from .
Step 7.3
Replace all occurrences of in with .
Step 7.4
Simplify the right side.
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Step 7.4.1
Simplify .
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Step 7.4.1.1
Simplify each term.
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Step 7.4.1.1.1
Multiply .
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Step 7.4.1.1.1.1
Combine and .
Step 7.4.1.1.1.2
Multiply by .
Step 7.4.1.1.2
Move the negative in front of the fraction.
Step 7.4.1.2
To write as a fraction with a common denominator, multiply by .
Step 7.4.1.3
Combine and .
Step 7.4.1.4
Combine the numerators over the common denominator.
Step 7.4.1.5
Simplify the numerator.
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Step 7.4.1.5.1
Multiply by .
Step 7.4.1.5.2
Add and .
Step 8
List all of the solutions.
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