# Linear Mappings Question

1. Jan 11, 2010

### DylanB

1. The problem statement, all variables and given/known data

http://img526.imageshack.us/img526/743/93134049.png [Broken]

2. Relevant equations
Just the standard linear mapping properties and theorums.

3. The attempt at a solution

I have already solved part A by considering the transformation A: Rn -> R | A(x) = a.x where x is a vector in Rn, and finding the dimension of the nullspace.

I am stuck on where to begin the proof for part b, once I have b I don't think I will have a problem generalizing it for part c.

Last edited by a moderator: May 4, 2017
2. Jan 11, 2010

### ystael

Your solution to part (a) already contains the essence of a solution to part (b); just think about the dimension of the null space of a different linear map $$B$$, one that uses the existence of $$\vec{a}$$ and $$\vec{b}$$ both.

(If you need a further hint: given that you are supposed to find that $$\dim(S \cap T) = n - 2$$ in case $$\vec{a}$$ and $$\vec{b}$$ are linearly independent, what do you think the dimension of the range space of $$B$$ ought to be?)

3. Jan 11, 2010

### DylanB

ah, thank you, very good. I have a transformation B: Rn -> R2 that works nicely, and the generalization follows quite easily.