# Linear Algebra Examples

Determine the Value of k for Which the System Has No Solutions
, ,
Step 1
Write the system of equations in matrix form.
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
Perform the row operation to make the entry at a .
Step 2.2.1
Perform the row operation 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
Since is undefined when , then makes the system have no solution.