In a $3\times3$ matrix can the vector $v$ belong to

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In a $3\times 3$ matrix, can the vector $v = \begin{pmatrix}1\\ 2\\ 3\end{pmatrix}$ belong to

a) both the column space and row space.

b) both the row space and null space.

c) both the column space and left null space.

d) both the column space and null space.

There can be multiple correct options.

At first, I thought the question was asking which spaces were equal, but it is actually asking for a specific vector. Any help would be greatly appreciated!

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HINT

a) both the column space and row space.

  • why not?

b) both the row space and null space.

  • what is $v^Tv$

c) both the column space and left null space.

  • what is $v^Tv$

d) both the column space and null space.

  • why not?