Find the null space of a matrix

mark

Find the null space of
$$
\left(\begin{matrix}
1 & 0 & 2 \\
0 & 1 & 0
\end{matrix}\right).
$$

Student16

$$
A = \left ( \begin{matrix}
1 & 0 & 2\\
0 & 1 & 0\\
\end{matrix} \right )
$$

$$\mathcal{N}(A) = \left \{ \begin{bmatrix} -2x_3 \\ 0 \\ x_3 \end{bmatrix} \middle| \, x_3 \in \mathbb{C} \right \}$$

Student26

is it ok to generalize the solution to:
$$N(A) = \left ( \begin{matrix}
-2\\
0\\
1\\
\end{matrix} \right ) $$

or to:
$$N(A) = \left ( \begin{matrix}
-2x\\
0x\\
1x\\
\end{matrix} \right ) $$

?

mark

@Student26 said:
is it ok to generalize the solution to:
$$N(A) = \left ( \begin{matrix}
-2\\
0\\
1\\
\end{matrix} \right ) $$

or to:
$$N(A) = \left ( \begin{matrix}
-2x\\
0x\\
1x\\
\end{matrix} \right ) $$

?

Well, the first one is definitely not correct - it's just a single vector, rather than an infinite set of vectors. We will learn soon (this week, in fact) about the span of a set of vectors and we might then answer this question as the span of the set containing that one vector.

The second one looks a bit better but I still don't think that it's clearly indicated that there is is a set of vectors there.