Hey MathStudent111111.
Hint: If it only spans V1 then it will only have scalar multiples of V1.
Hi,
I'm having trouble with this subject and would like to ask for some help and explanations.
For example, I have the following question:
V1 = (1,1,1)
V2 = (2,3,1)
Find linear transformation T:R3 -> R3 such that:
a. Its kernel spans by V1 and V2
b. Its kernel span by V1 only
How should I approach this?
Any help will be appreciated.
Thanks
Just recall that a linear transformation is completely determined if we know the image of the vectors in any base of the domain.
So, first of all, find a third vector so that is a base for
A. You want the kernel of to be the span of therefore you need to set and Additionally, you have to make non-zero (this way you don't get a bigger kernel).
B. Set and send and to two non-zero linearly independent vectors in say, and