Linear Algebra Examples

Write as a Vector Equality -4+y=4 , 4x-y=4
,
Step 1
Add to both sides of the equation.
Step 2
Add and .
Step 3
Write the system of equations in matrix form.
Step 4
Find the reduced row echelon form.
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Step 4.1
Swap with to put a nonzero entry at .
Step 4.2
Multiply each element of by to make the entry at a .
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Step 4.2.1
Multiply each element of by to make the entry at a .
Step 4.2.2
Simplify .
Step 4.3
Perform the row operation to make the entry at a .
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Step 4.3.1
Perform the row operation to make the entry at a .
Step 4.3.2
Simplify .
Step 5
Use the result matrix to declare the final solutions to the system of equations.
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.