Exam 1 question 4 asks for the all possible reduced row echelon forms of R of all 3x3 matrices. Why isn't the matrix
111
000
000
included as a basis? See
http://ocw.mit.edu/courses/mathematics/18-06sc-linear-algebra-fall-2011/ax-b-and-the-four-subspaces/exam-1/MIT18_06SCF11_ex1s.pdf
Thanks

Question

Exam 1 question 4 asks for the all possible reduced row echelon forms of R of all 3x3 matrices. Why isn't the matrix
111
000
000
included as a basis?  See
http://ocw.mit.edu/courses/mathematics/18-06sc-linear-algebra-fall-2011/ax-b-and-the-four-subspaces/exam-1/MIT18_06SCF11_ex1s.pdf
Thanks

joshdanziger23 · Answer

Dbwonders, I see that the proposed basis in the examiners' solutions includes [100; 000; 000], [110; 000; 000] and [101; 000; 000]. The matrix you propose is a linear combination of these three,  so it is implicitly included. Do you think it would be better if it was explicitly included? Josh.

anonymous · Answer

It's so obvious now! If you look at the matrices as vectors it is so clear! Thanks for taking the time to answer.