Linear Algebra Examples

Write as a Vector Equality 3x-y=9 , -6x+2y=-18
,
Step 1
Write the system of equations in matrix form.
Step 2
Row reduce to eliminate one of the variables.
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Step 2.1
Multiply each element of by to make the entry at a .
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Step 2.1.1
Multiply each element of by to make the entry at a .
Step 2.1.2
Simplify .
Step 2.2
Perform the row operation to make the entry at a .
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Step 2.2.1
Perform the row operation to make the entry at a .
Step 2.2.2
Simplify .
Step 3
Use the result matrix to declare the final solutions to the system of equations.
Step 4
Solve the equation for .
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Step 4.1
Subtract from both sides of the equation.
Step 4.2
Multiply both sides of the equation by .
Step 4.3
Simplify both sides of the equation.
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Step 4.3.1
Simplify the left side.
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Step 4.3.1.1
Simplify .
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Step 4.3.1.1.1
Cancel the common factor of .
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Step 4.3.1.1.1.1
Move the leading negative in into the numerator.
Step 4.3.1.1.1.2
Factor out of .
Step 4.3.1.1.1.3
Cancel the common factor.
Step 4.3.1.1.1.4
Rewrite the expression.
Step 4.3.1.1.2
Multiply.
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Step 4.3.1.1.2.1
Multiply by .
Step 4.3.1.1.2.2
Multiply by .
Step 4.3.2
Simplify the right side.
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Step 4.3.2.1
Simplify .
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Step 4.3.2.1.1
Apply the distributive property.
Step 4.3.2.1.2
Multiply.
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Step 4.3.2.1.2.1
Multiply by .
Step 4.3.2.1.2.2
Multiply by .
Step 4.4
Reorder and .
Step 5
The solution is the set of ordered pairs that makes the system true.
Step 6
Decompose a solution vector by re-arranging each equation represented in the row-reduced form of the augmented matrix by solving for the dependent variable in each row yields the vector equality.