Chapter 4.2, Problem 8P

PROBLEMS

For Problems 1-14, determine whether the given set $S$ of vectors is closed under addition and closed scalar multiplication. In each case, take the set of scalars to be the set of all real numbers.

For fixed $m\times n$ matrix $\text{A}$, the set,

$S:=\left\{x\in {ℝ}^n:\text{A}x=0\right\}$.

(This is the set of all solutions to the homogeneous linear system of equation $\text{A}x=\text{0}$ and is often called the null space of $\text{A}$.)