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I have a vector $V$. I project $V$ to its left null space by multiplying it with matrix $A$. $V$ represents $(x, y)$ coordinates of a point in $2D$ space. What would be physical interpretation of this? thanks

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In your notation, the left null space of a vector $V\in \mathbb{R}$ is the matrix $A$ such that $AV = 0$. On the $2d$ plane $A$ represents the vector orthogonal to $V$ (but if $V$ is a zero vector $A$ is formed by the basis on $2d$ plane).

So, projecting $V$ to its left null space will result in zero, because $V$ is orthodonal to it by definition.

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    Yes, it is zero. But what would be the physical interpretation? like now my coordinates denote the $(0,0)$? – 2017-02-24
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    @IsamAbdullah, yes, exactly. Projection results in receiving zero vector. – 2017-02-24