Linear Algebra Examples

Write as a Vector Equality -x+3y=-6 , x=6+3y
,
Step 1
Subtract from both sides of the equation.
Step 2
Write the system of equations in matrix form.
Step 3
Row reduce to eliminate one of the variables.
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Step 3.1
Multiply each element of by to make the entry at a .
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Step 3.1.1
Multiply each element of by to make the entry at a .
Step 3.1.2
Simplify .
Step 3.2
Perform the row operation to make the entry at a .
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Step 3.2.1
Perform the row operation to make the entry at a .
Step 3.2.2
Simplify .
Step 4
Use the result matrix to declare the final solutions to the system of equations.
Step 5
Solve the equation for .
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Step 5.1
Subtract from both sides of the equation.
Step 5.2
Divide each term in by and simplify.
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Step 5.2.1
Divide each term in by .
Step 5.2.2
Simplify the left side.
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Step 5.2.2.1
Cancel the common factor of .
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Step 5.2.2.1.1
Cancel the common factor.
Step 5.2.2.1.2
Divide by .
Step 5.2.3
Simplify the right side.
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Step 5.2.3.1
Simplify each term.
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Step 5.2.3.1.1
Divide by .
Step 5.2.3.1.2
Dividing two negative values results in a positive value.
Step 6
The solution is the set of ordered pairs that makes the system true.
Step 7
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.