Linear Algebra Examples

Write as a Vector Equality y=x-4 , x+3y=12
,
Step 1
Subtract from both sides of the equation.
Step 2
Write the system of equations in matrix form.
Step 3
Find the reduced row echelon form.
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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 3.3
Multiply each element of by to make the entry at a .
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Step 3.3.1
Multiply each element of by to make the entry at a .
Step 3.3.2
Simplify .
Step 3.4
Perform the row operation to make the entry at a .
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Step 3.4.1
Perform the row operation to make the entry at a .
Step 3.4.2
Simplify .
Step 4
Use the result matrix to declare the final solutions to the system of equations.
Step 5
The solution is the set of ordered pairs that makes the system true.
Step 6
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.