# Math Help - T-invariant subspace;inner product

1. ## T-invariant subspace;inner product

In R^2 with the standard dot product, define T(x,y)=(2x+y,0). Find a subspace U of R^2 such that U is T-invariant but U orthogonal is not T-invariant. Does T fix all the vectors in the subspace U you found?

I'm not really sure where to even start with this problem, any help would be appreciated!! thank you.

2. You might note that you can generate a $T$-invariant subspace by taking a vector $x\in V$ and taking the basis $\{x, Tx, T^2x, T^3x,\ldots\}$.