Examples

Minimize the Equation given the Constraints
,
Step 1
Introduce slack variables and to replace the inequalities with equations.
Step 2
Subtract from both sides of the equation.
Step 3
Subtract from both sides of the equation.
Step 4
Add to both sides of the equation.
Step 5
Write the system of equations in matrix form.
Step 6
Find the reduced row echelon form.
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Step 6.1
Perform the row operation to make the entry at a .
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Step 6.1.1
Perform the row operation to make the entry at a .
Step 6.1.2
Simplify .
Step 6.2
Multiply each element of by to make the entry at a .
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Step 6.2.1
Multiply each element of by to make the entry at a .
Step 6.2.2
Simplify .
Step 6.3
Perform the row operation to make the entry at a .
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Step 6.3.1
Perform the row operation to make the entry at a .
Step 6.3.2
Simplify .
Step 7
Use the result matrix to declare the final solutions to the system of equations.
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