Originally Posted by
Theaisback Hey everyone,
I'm stuck on this question I'll show you what I got so far, but first I'll write out the question...
Let A = |2 4 -5|.Which of the following vectors belongs to the null space of A?
|1 3 -3|
u1 = (1, 2, 3), u2 = (3, 1, 2), u3 = (0, 0, 0), u4 = (0, 0), u5 = (6, 2, 4)
|2 4 -5 | R1 --> 1/2 * R1
|1 3 -3 |
|1 2 -5/2|
|1 3 -3 | R2 --> -1 * R1 + R2
|1 2 -5/2| R1 ---> -2 * R2 + R1
|0 1 -1/2|
|1 0 -3/2|
|0 1 -1/2|
this corresponds to the system
1x1 +(-3/2)x3 = 0
1x2 +(-1/2)x3 = 0
the system has infinitely many solutions:
x1 = +(3/2) x3
x2 = +(1/2) x3
the solution can be written in vector form:
(3/2, 1/2, 1) therefore the null space has a basis formed by this set.
This is what I got, but I do not know how to use the U1, U2, U3, U4, U5 from the question above. Did I make a mistake or what?
Thanks for you help!