Which of the following is a vector in null A, where $A=\begin{bmatrix}3&4\\6&8\\\end{bmatrix}$

$$\begin{bmatrix}4&-3\end{bmatrix}^T$$ $$\begin{bmatrix}2&2\end{bmatrix}^T$$ $$\begin{bmatrix}-1&1\end{bmatrix}^T$$ $$\begin{bmatrix}3&-4\end{bmatrix}^T$$

I was wondering is there a certain formula on how to solve this.I'm reading my textbook under the subspaces and spanning but i cannot find any example relating to this question

  • 1
    $\begingroup$ By definition, the null space of $A$ consists of those vectors $X$ such that $AX=0$. Just multiply each of your possibilities with $A$ and see if the result of any of them is the zero vector! $\endgroup$ – Henning Makholm Nov 22 '15 at 23:45
  • $\begingroup$ Or solve the system $3x + 4y = 0 \quad 6x + 8y = 0$. $\endgroup$ – pjs36 Nov 22 '15 at 23:46
  • $\begingroup$ Oh thank you both @HenningMakholm and pjs36 $\endgroup$ – Micky Nov 22 '15 at 23:48
  • $\begingroup$ You can find a basis for the null space of a matrix via row-reduction, but for this problem it’s easy enough to multiply each of the vectors in turn. $\endgroup$ – amd Nov 23 '15 at 2:43

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