Linear Algebra

Step 1: Representing the system in augmented matrix form
The given system of equations can be written in matrix form as: Step 2: Row reduction
Performing row operations to convert the augmented matrix into row echelon form: 1. Make the first pivot 1 (it is already 1 in the first row). 2. Subtract (Row 1) from Row 2. 3. Subtract (Row 1) from Row 3. After performing these operations, we get: Adding Row 2 and Row 3 to eliminate the second column entry in Row 3: Step 3: Checking for inconsistency
The last row corresponds to the equation: which is a contradiction (since ). This indicates that the system has no solution. Step 4: Conclusion
Since the system is inconsistent, it has no solution.