Thread: Linear Algebra question

Show that the non zero rows of an echelon form matrix form a linearly independent set.

That’s what it is?

(1) (0) (0) = (0)
c1(0) + c2 (1) +c3 (0) = (0) so c1=0, c2=0, c3=0
(0) (0) (1) = (0)

again

1 0 0 0
c1 0 + c2 1 + c3 0 = 0 so c1 = 0, c2=0 and c3=o----->independent
0 0 1 0

I think you are trying to write

and derive from that that those vectors are independent. But that is the identity matrix, not a general "row echelon matrix". A three by three row echelon matrix would be of the form:

so you should be looking at
.

Also, I see nothing in your question that restricts this to 3 by 3 matrices. You should be able to do a general proof.