8th Ed, 1.5, Exercise 12

Show that if A =
100
010
abc
is an elementary matrix,
then at least one entry in the third row must be a zero — but not c.

[Hints: Can A be elementary if c = 0?
If 0 ≠ c ≠ 1, what more can be said about a and b?
And what, finally, if instead c = 1?]

First posted: 05 Feb 2006.

Valid HTML 4.01 Transitional