- #1
andrey21
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Find bases for the kernal of the following:
T(x1,x2,x3,x4) = (x1+x2+x3,-x3,x1+x2)
Any help would be great thank you
T(x1,x2,x3,x4) = (x1+x2+x3,-x3,x1+x2)
Any help would be great thank you
Yes, good! So you haveIt is the set of vectors in the domain for which T(v) = 0 correct???
Ah is it x1(000)??
Ah brilliant with there being no basis for the kernal is tht like saying it has a dimension of 0??
Any vector in the kernel is of that form. Strictly speaking a 'basis" is a set of vectors: {(2, 1, 0), (0, 0, 1)}.I know this is an old thread but I have a similar question I wish to ask.
Find the basis for the kernel of the following:
T_{3}(x,y,z) = (x-2y,3x-6y)
so
x-2y=0 (1)
x=2y
3x-6y=0 (2)
Therefore (2) becomes:
3(2y)-6y=0
6y=6y
y=y
So the basis for kernel is:
y(2,1,0)+z(0,0,1)
is this correct??