I'm having difficulty with this question:
Let V be a subspace of $\mathbb R^4$ spanned by the set $U = {(1, -1, 3, 1), (2, 1, -1, 2), (-1, 3, 0, 2)}$. Show that U is a basis of V and determine whether the vector $t = (-3, 6, 7, 6)$ belongs to space V in order to find the coordinate vector of $t$ relative to basis $U$.
My problem is that although the vectors are linearly independent with the trivial solution $c$1 = $c$2 = $c$3 = $0$, I did not think it was possible to span $\mathbb R^4$ with only 3 vectors.
I assume $t$ can be found by equating the vectors in $U$ to $t$ for the $b$ column of the matrix, but how can a coordinate vector be found if it seems that $U$ is not a basis of $V$? Or have I made a wrong assumption?