5-t should be 5+t
Fragment of a discussion from Science talk:Math Exam Resources/Courses/MATH221/December 2011/Question 1 (a)
Thanks for adding this additional line. In the last step, when adding L2+L3 we would now get [0,0,t,-1], not [0,0,-1+t,-1], so that again the solutions needs to be adjusted! In fact, I would also like to see how you get back from the reduced matrix to the linear system to conclude consistency (x3 equation is enough).