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**Homework Statement**

Give a specific example of an operator T on R^4 such that,

1. dim(nullT) = dim(rangeT) and

2. dim(the intersection of nullT and rangeT) = 1

**The attempt at a solution**

I know that dim(R^4) = dim(nullT) + dim(rangeT) = 4, so dim(nullT) = dim(rangeT) = 2.

I also know that nullT will have 2 basis vectors and rangeT will also have 2 basis vectors (so that 1. is satisfied), and that they must have one vector in common (so that 2. is satisfied).

I started with T(w, x, y, z) = (w, x, 0, 0), but that only does it halfway.

I just don't know how to generate an example that satisfies both conditions.

Any ideas?