00:01
Okay, so we have this matrix a.
00:02
We want to find k such that the null space of a is a subspace of rk, and we want to find k such that the column space is a subspace of rk.
00:13
Okay, so firstly for part a, let's think about what sort of vectors this matrix operates on, or acts on, minus 597, minus 1 ,17.
00:27
Well, there's three columns, so it has to act on a matrix with, three components, say x, y, z.
00:34
So the outcome would be minus 5x plus 9y plus 7 z, minus x plus y plus 7 z.
00:48
And the nonspace is a subspace of the domain, and the domain here is r3.
00:54
So the domain is r3, vectors of length 3.
01:00
The nonspace is a subspace of r3...