let V 10-dimensional and W is 7-dimensional and N be 4- dimensional then prove that there is a set...

Question

let V 10-dimensional and W is 7-dimensional and N be 4- dimensional then prove that there is a set of T:V --> W such that N subset of NullT and find the dim of this set.

David · Accepted Answer

Let {n1, . . . , n4} be a basis forN and extend this to a basis {n1, . . . , n4, v1, . . . , v6}
for V . Let {w1, . . . , w7} be a basis for W . Define T : V → W by T (ni) = 0 for
1 ≤ i ≤ 4 and T (vi) = wi if 1 ≤ i ≤ 6. Then extend T be linearity. That is,

let V 10-dimensional and W is 7-dimensional and N be 4- dimensional then prove that there is a set of T:V --> W such that N subset of NullT and find the dim of this set.

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