# What is the image of a vector?

So I did part A which is pretty straight forward. Though I'm confused when it says "images of the vectors" in part b. Not exactly sure what that is referring to. Is that like shading an area underneath the vector or what? I can't find "image of a vector" anywhere into google. It just comes up with "graphic stock vector images" which isn't related to math. Any ideas?

The relevant meaning of image is an aspect of functions, so what the question's actually asking for is the result of applying the matrix $$A$$ to the vectors and points given. It could have been more clearly phrased as the "image of the vectors under the transform $$A$$" - and for any other term, Google probably would have been able to tell you that, but unfortunately the other meaning of vector in computer graphics flooded out the results

• awesome thanks. so how would I draw that? when you said "result of applying the matrix" does that mean you add the matrix to the points in an augmented matrix? or do I add the values or something and redraw the vectors? Sep 20, 2020 at 16:07
• By "applying the matrix" I mean calculating the transform/function the matrix represents, what the question calls $T(v)$, using those values as inputs. (Augmented matrice are a different thing) $T([1, 0])$ will give you another vector, which you can draw on your diagram at the point corresponding to its x and y components Sep 20, 2020 at 16:15
• Awesome thanks! Sep 20, 2020 at 16:16
• As a hint, $T([3,2])$ is $[8,1]$, which is technically a vector, but can interchangeably be treated as a point 8 units along the x-axis and 1 up the y-axis. If you don't understand how I got that answer, read more about the transforms matrices represent and how to multiply vectors by matrices Sep 20, 2020 at 16:21
• I will definitely look into transformations! I have 0 clue how you got that answer lol Sep 20, 2020 at 16:22

If $$f:A\to B$$ is a function, the image by $$f$$ of the element $$a\in A$$ is $$f(a)$$. The image by $$f$$ of a subset $$U\subseteq A$$ is the set $$f[U]:=\{f(x)\,:\, x\in U\}\subseteq B$$.

• Gonna be honest I have no idea what that means. I do recognize that walrus operator := from python 3.8 Sep 20, 2020 at 16:08
• $:=$ is just a semi-stanard shorthand for saying that the equality of interest is actually a definition. For the rest, you can reference the Wikipedia article in the other guy's answer.
– user239203
Sep 20, 2020 at 16:17