Given the augmented matrix (121∣5013∣2000∣k)\begin{pmatrix} 1 & 2 & 1 & | & 5 \\ 0 & 1 & 3 & | & 2 \\ 0 & 0 & 0 & | & k \end{pmatrix}100210130∣∣∣52k, for what value of kkk is the system consistent?
k=1k = 1k=1
k=0k = 0k=0
k=−1k = -1k=−1
Any value except 000