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## 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