Science talk:Math Exam Resources/Courses/MATH221/April 2013/Question 06

Once we've gotten all the way to the end...should there still be a lingering negative from the first expansion along the 4th row? Yes or no?

Solution overhaul - recheck please!

Thanks a bunch. It looks good. I re-did the computations using Sage:

B = matrix(QQ, 5,5,[[1,2,2,-1,3],[2,6,3,-3,7],[-3,-4,-3,2,-8],[-2,-6,-2,2,-7],[1,-2,7,3,3]]) print B, '\n' B.add_multiple_of_row(3,1,1) print B, '\n' B.add_multiple_of_row(1,0,-2), B.add_multiple_of_row(2,0,3), B.add_multiple_of_row(4,0,-1) print B, '\n' B.add_multiple_of_row(2,1,-1), B.add_multiple_of_row(4,1,2) print B, '\n' B.add_multiple_of_row(2,3,-4), B.add_multiple_of_row(4,3,-3) print B, '\n' B.swap_rows(2,3) print B, '\n' B.add_multiple_of_row(4,3,-5/4) print B, '\n'

You can then also do things like: print latex(B) \left(\begin{array}{rrrrr} 1 & 2 & 2 & -1 & 3 \\ 0 & 2 & -1 & -1 & 1 \\ 0 & 0 & 1 & -1 & 0 \\ 0 & 0 & 0 & 4 & 0 \\ 0 & 0 & 0 & 0 & 2 \end{array}\right)

and most of the work is done for us. Will do this next time.