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Linear Algebra Examples
, ,
Step 1
Write the system of equations in matrix form.
Step 2
Step 2.1
Divide by .
Step 2.2
Divide by .
Step 2.3
Divide by .
Step 2.4
Multiply by .
Step 2.5
Divide by .
Step 2.6
Divide by .
Step 2.7
Divide by .
Step 2.8
Cancel the common factor of .
Step 2.8.1
Cancel the common factor.
Step 2.8.2
Rewrite the expression.
Step 2.9
Multiply by .
Step 2.10
Divide by .
Step 2.11
Divide by .
Step 2.12
Perform the row operation to make the entry at a .
Step 2.12.1
Perform the row operation to make the entry at a .
Step 2.12.2
Simplify .
Step 2.13
Perform the row operation to make the entry at a .
Step 2.13.1
Perform the row operation to make the entry at a .
Step 2.13.2
Simplify .
Step 2.14
Multiply each element of by to make the entry at a .
Step 2.14.1
Multiply each element of by to make the entry at a .
Step 2.14.2
Simplify .
Step 2.15
Perform the row operation to make the entry at a .
Step 2.15.1
Perform the row operation to make the entry at a .
Step 2.15.2
Simplify .
Step 2.16
Multiply each element of by to make the entry at a .
Step 2.16.1
Multiply each element of by to make the entry at a .
Step 2.16.2
Simplify .
Step 2.17
Perform the row operation to make the entry at a .
Step 2.17.1
Perform the row operation to make the entry at a .
Step 2.17.2
Simplify .
Step 2.18
Perform the row operation to make the entry at a .
Step 2.18.1
Perform the row operation to make the entry at a .
Step 2.18.2
Simplify .
Step 2.19
Perform the row operation to make the entry at a .
Step 2.19.1
Perform the row operation to make the entry at a .
Step 2.19.2
Simplify .
Step 3
Use the result matrix to declare the final solutions to the system of equations.
Step 4
The solution is the set of ordered pairs that makes the system true.
Step 5
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.