Linear Algebra Examples

Solve the Matrix Equation a[[1],[-2]]+b[[3],[-2]]=[[-2],[1]]
Step 1
Simplify each term.
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Step 1.1
Multiply by each element of the matrix.
Step 1.2
Simplify each element in the matrix.
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Step 1.2.1
Multiply by .
Step 1.2.2
Move to the left of .
Step 1.3
Multiply by each element of the matrix.
Step 1.4
Simplify each element in the matrix.
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Step 1.4.1
Move to the left of .
Step 1.4.2
Move to the left of .
Step 2
Add the corresponding elements.
Step 3
Write as a linear system of equations.
Step 4
Solve the system of equations.
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Step 4.1
Subtract from both sides of the equation.
Step 4.2
Replace all occurrences of with in each equation.
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Step 4.2.1
Replace all occurrences of in with .
Step 4.2.2
Simplify the left side.
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Step 4.2.2.1
Simplify .
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Step 4.2.2.1.1
Simplify each term.
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Step 4.2.2.1.1.1
Apply the distributive property.
Step 4.2.2.1.1.2
Multiply by .
Step 4.2.2.1.1.3
Multiply by .
Step 4.2.2.1.2
Subtract from .
Step 4.3
Solve for in .
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Step 4.3.1
Move all terms not containing to the right side of the equation.
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Step 4.3.1.1
Subtract from both sides of the equation.
Step 4.3.1.2
Subtract from .
Step 4.3.2
Divide each term in by and simplify.
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Step 4.3.2.1
Divide each term in by .
Step 4.3.2.2
Simplify the left side.
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Step 4.3.2.2.1
Cancel the common factor of .
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Step 4.3.2.2.1.1
Cancel the common factor.
Step 4.3.2.2.1.2
Divide by .
Step 4.3.2.3
Simplify the right side.
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Step 4.3.2.3.1
Move the negative in front of the fraction.
Step 4.4
Replace all occurrences of with in each equation.
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Step 4.4.1
Replace all occurrences of in with .
Step 4.4.2
Simplify the right side.
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Step 4.4.2.1
Simplify .
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Step 4.4.2.1.1
Multiply .
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Step 4.4.2.1.1.1
Multiply by .
Step 4.4.2.1.1.2
Combine and .
Step 4.4.2.1.1.3
Multiply by .
Step 4.4.2.1.2
To write as a fraction with a common denominator, multiply by .
Step 4.4.2.1.3
Combine and .
Step 4.4.2.1.4
Combine the numerators over the common denominator.
Step 4.4.2.1.5
Simplify the numerator.
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Step 4.4.2.1.5.1
Multiply by .
Step 4.4.2.1.5.2
Add and .
Step 4.5
List all of the solutions.