A linear system with three variables has augmented matrix that is row-equivalent to the 
following matrix: 

k + 3 2 k − 4 = 3 
0 2 −9 = 5 
0 0 k^2 + k − 2 = k − 1 
Determine the values of k for which the system has: 
(a) exactly one solution, 
(b) infinitely many solutions, 
(c) no solutions.

(a) Write down the augmented matrix corresponding to the linear system: 
4x1 + 2x2 − 7x3 − 11x4 = 5 
2x1 + 1x2 − 2x3 − 4x4 = 2 
4x1 + 2x2 − 10x3 − 14x4 = 6 

(b) Use Gauss-Jordan elimination to reduce this matrix to reduced row-echelon form. 


(c) Solve the linear system.