With A the matrix that is shown below, write A as a
product of elementary matrices.
1
2
3
2
5
6
1
3
4
Show or explain your reasoning.
Prove the following proposition (labeled Lemma in 2/14 class
notes and slightly reworded here).If kB=0, for some real number k
and some matrix B, then either k = 0 or B = 0.
Here's the proof outline suggested in class.
Assume that k and B are a real number and a matrix,
respectively, for which kB = 0.
It suffices to show that if k is not zero, then B must
be the zero matrix.
Assume k is not zero.
Provide reasoning to eventually conclude that B is the
zero matrix.
Side note (not literally assigned). For practice, you might
find it interesting/useful to construct some other possible
outlines for proving a statement of the form P ==> (Q or R).
The one given here is, of course: Assume P. Assume not Q. Show
R. What are some other possibilities?