Chapter 5.2, Problem 11E

Prove: If A is an $m\times n$ matrix and $x\in {ℝ}^n,$ then either $Ax=0$ or there exists $t\in R{\left(A\right)}^T$ such that $x^{T}y\ne 0.$ Draw a picture similar to Figure 5.2.2 to illustrate this result geometrically for the case where $N\left(A\right)$ isatwo-dimensionalsubspaceof ${ℝ}^3.$