# Linear Algebra Examples

Solve Using a Matrix by Row Operations
, ,
Step 1
Write the system as a matrix.
Step 2
Find the reduced row echelon form.
Step 2.1
Perform the row operation to make the entry at a .
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 .
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 .
Step 2.3.1
Perform the row operation to make the entry at a .
Step 2.3.2
Simplify .
Step 2.4
Multiply each element of by to make the entry at a .
Step 2.4.1
Multiply each element of by to make the entry at a .
Step 2.4.2
Simplify .
Step 2.5
Perform the row operation to make the entry at a .
Step 2.5.1
Perform the row operation to make the entry at a .
Step 2.5.2
Simplify .
Step 2.6
Perform the row operation to make the entry at a .
Step 2.6.1
Perform the row operation to make the entry at a .
Step 2.6.2
Simplify .
Step 2.7
Perform the row operation to make the entry at a .
Step 2.7.1
Perform the row operation to make the entry at a .
Step 2.7.2
Simplify .
Step 3
Use the result matrix to declare the final solution to the system of equations.
Step 4
The solution is the set of ordered pairs that make the system true.
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