# Why is the resultant of this $0$? What is this property called?

I have two column vecotors $A$ and $B$. I multiply all the corresponding elements of $A$ with the corresponding elements of $B$ and call the result $x$. Now I sum all the elements of $x$ and subtract the result from $B$ (from what I presume is all the elements of $B$). This result is in turn is multipled with $A$ again to give the final answer of $0$. Why is this the case? Is there a particular name to this property of vectors?

Below is a MATLAB exercise screenshot of where I am getting this particular question. $A$ is x' and $B$ is y'

• If any mod sees this, please could you actually post the picture from the link, into the question ? I do not have enough reputation for this!
– SDG
Nov 26, 2015 at 18:26
• I'm sure that you have something in your notes or textbook about the dot product.... Nov 26, 2015 at 20:16

The actions described in steps (d) and (e) are the definition of "*" in step (f)$: $$\begin{bmatrix}x_1&x_2&\cdots&x_n\end{bmatrix}*\begin{bmatrix}y_1\\y_2\\\vdots\\y_n\end{bmatrix} := [x_1y_1 + x_2y_2 + \cdots + x_ny_n]$$ That your difference was$0\$ simply tells you that you didn't goof up, and neither did the machine.