- #1
PhyStan7
- 18
- 0
Homework Statement
Let A = 1 3 2 2
1 1 0 -2
0 1 1 2
Viewing A as a linear map from M_(4x1) to M_(3x1) find a basis for the kernal of A and verify directly that these basis vectors are indeed linearly independant.
The Attempt at a Solution
Ok so first i found the reduced row echelon form of A. This equals:
rref(A) =
1 0 -1 -4
0 1 1 2
0 0 0 0
So i found the kernal of this by-
1 0 -1 -4
0 1 1 2
0 0 0 0
Multiplied by
x_1
x_2
x_3
x_4
Equals
0
0
0
0.
x_1 = x_3 + x_4
x_2 = -x_3-2x_4
x_3 = x_3
x_4 = x_4
Therefore kernal...
=x_3 {1, -1, 1, 0} + x_4 {1, -2, 0, 1}
So i thought this meant the basis equalled
Basis of kernal = (1,-1,1,0),(1,-2,0,1)
I have idea what to do now though. I have no idea if what i have done is vaguely right and am not sure if it is how to fulfill the rest of the question. The problem is i have not really incoperated the fact that in the question it states that Viewing A as a linear map from M_(4x1) to M_(3x1). I do not understand this terminology, what does it mean exactly?
(ps - i appologise for the bad formatting)
Thanks