# Thread: V,W have basis and dim(null(t))

1. ## V,W have basis and dim(null(t))

Hello, I can't seem to figure out this problem about linear maps:

Assume v1,v2,..v5 is a basis of V and w1,w1,...w6 is a basis of W. Suppose you need to define a linear map T: V --> W. Which values would you assign to T(v1),T(v2),..T(v5) if it is required that dim(Null(T))=3, and that w1 is not in range(T).

I was wondering if the values of T(v1),..T(v5) should be scalars, or be variables with respect to w.

Thank you!!

2. Originally Posted by jax
Hello, I can't seem to figure out this problem about linear maps:

Assume v1,v2,..v5 is a basis of V and w1,w1,...w6 is a basis of W. Suppose you need to define a linear map T: V --> W. Which values would you assign to T(v1),T(v2),..T(v5) if it is required that dim(Null(T))=3, and that w1 is not in range(T).

I was wondering if the values of T(v1),..T(v5) should be scalars, or be variables with respect to w.

Thank you!!
??? You just said, T is a linear map from V to W. No, T(v1), etc. are NOT numbers, nor are they "variables with respect to W" (whatever that might mean). T(v1) etc. are vectors in W. That' is exactly what "T is a linear map from V to W" means.

3. I found the answer and actually they were numbers and vectors with respect to w. So you were wrong, but thanks anyways

T(v1)=0
t(v2)=0
t(v3)=0
t(v4)=w2+w3
t(v5)=w4+w5+w6