Linear Algebra Examples

Write as a Vector Equality x-y=7 , 2x-2y=k
,
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.
Tap for more steps...
Step 3.1
Swap with to put a nonzero entry at .
Step 3.2
Multiply each element of by to make the entry at a .
Tap for more steps...
Step 3.2.1
Multiply each element of by to make the entry at a .
Step 3.2.2
Simplify .
Step 3.3
Perform the row operation to make the entry at a .
Tap for more steps...
Step 3.3.1
Perform the row operation to make the entry at a .
Step 3.3.2
Simplify .
Step 4
Use the result matrix to declare the final solutions to the system of equations.
Step 5
Add to 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.