Linear Algebra Examples

Write as a Vector Equality x+y+z+w=15 , x-2y+4z-w=12
,
Step 1
Write the system of equations in matrix form.
Step 2
Find the reduced row echelon form.
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Step 2.1
Perform the row operation to make the entry at a .
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Step 2.1.1
Perform the row operation to make the entry at a .
Step 2.1.2
Simplify .
Step 2.2
Multiply each element of by to make the entry at a .
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Step 2.2.1
Multiply each element of by to make the entry at a .
Step 2.2.2
Simplify .
Step 2.3
Perform the row operation to make the entry at a .
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Step 2.3.1
Perform the row operation to make the entry at a .
Step 2.3.2
Simplify .
Step 3
Use the result matrix to declare the final solutions to the system of equations.
Step 4
Move all terms not containing to the right side of the equation.
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Step 4.1
Subtract from both sides of the equation.
Step 4.2
Add to both sides of the equation.
Step 5
Move all terms not containing to the right side of the equation.
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Step 5.1
Add to both sides of the equation.
Step 5.2
Subtract from both sides of the equation.
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.