Two matrices A and B are called row -equivalent (written A - B) if there is a sequence of elementary row operations carrying A to B.
(a) Show that A - B if and only if A = UB for some invertible matrix U.
(b) Show that:
(i) A - A for all matrices A.
(ii) ISA - B, then B - A.
(iii) If A - B and B - C, then A - C.
(c) Show that, if A and B are both row- equivalent to some third matrix, then A - B.
(d) Show that

are row-equivale.

Transcribed Image Text:

1-1 3 2 0 141 and-21-1-8 1 0 8 6 1-1 4 S -1 2 22