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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???
Yup. To be more precise, the only coordinate that is in the kernal is (0,0,0). You could even loosely say that there is no basis for the kernal.Ah is it x1(000)??
Anything with no variation will be dimensionless.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??