Given $U = \operatorname{span} \{(1; -1; 2; 0), (3, 0, 1, m), (1, 2, -3, 0)\}$ If $\dim(U^\perp) = 2\}$
Find $m$.
I don't sure how to solve this problem. Here is my idea:
Because $\dim(U^\perp) + \dim(U) = n$, if $U$ is a subspace of $\mathbb R^n$ And I guess $U$ is subspace of $\mathbb R^4$, so, $\dim(U)$ will be equal to $2$. After that, so after transform U to reduce echelon matrix, will contain exactly $2$ leading one.
I don't sure this way is true or wrong.
Thanks :)