Linear Algebra Examples

Write as a Vector Equality -x+y+z=0 , 12-250y+680z=0 , 10-100x-680=0
, ,
Step 1
Subtract from both sides of the equation.
Step 2
Subtract from .
Step 3
Add to both sides of the equation.
Step 4
Write the system of equations in matrix form.
Step 5
Find the reduced row echelon form.
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Step 5.1
Multiply each element of by to make the entry at a .
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Step 5.1.1
Multiply each element of by to make the entry at a .
Step 5.1.2
Simplify .
Step 5.2
Perform the row operation to make the entry at a .
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Step 5.2.1
Perform the row operation to make the entry at a .
Step 5.2.2
Simplify .
Step 5.3
Multiply each element of by to make the entry at a .
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Step 5.3.1
Multiply each element of by to make the entry at a .
Step 5.3.2
Simplify .
Step 5.4
Perform the row operation to make the entry at a .
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Step 5.4.1
Perform the row operation to make the entry at a .
Step 5.4.2
Simplify .
Step 5.5
Multiply each element of by to make the entry at a .
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Step 5.5.1
Multiply each element of by to make the entry at a .
Step 5.5.2
Simplify .
Step 5.6
Perform the row operation to make the entry at a .
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Step 5.6.1
Perform the row operation to make the entry at a .
Step 5.6.2
Simplify .
Step 5.7
Perform the row operation to make the entry at a .
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Step 5.7.1
Perform the row operation to make the entry at a .
Step 5.7.2
Simplify .
Step 5.8
Perform the row operation to make the entry at a .
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Step 5.8.1
Perform the row operation to make the entry at a .
Step 5.8.2
Simplify .
Step 6
Use the result matrix to declare the final solutions to the system of equations.
Step 7
The solution is the set of ordered pairs that makes the system true.
Step 8
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.