5-t should be 5+t

The solution shows 5-t when it should be 5+t, in the first line. Also, for clarity, I would like to see the additional step of multiplying the second row by -1. This also affects the solution of 1b).

Also, in the question, the second row has 2 for the coefficient of x3 in the second row. The solution to 1a uses 3 instead of 2. That probably changes the solution.

Thanks guys! I've made the corrections and added the details Bernhard asked. Let me know.

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).

Wow! I need to watch out that code a bit more closely. Thanks for your carful work!

I've corrected the solution and added the line you asked. (I also checked in wolfram alpha and the solution is now correct)