FP1 matrix question

So this type of question is my main problem in FP1.
In Q4c, why R=QP but not R=PQ? What is the difference between them?

Think of it like a function. A matrix is a "function" that you feed it in a point and it gives out a point.

So QP = Q(P), that is you feed Q the "point"/"matrix" P and not the other way around, basically think of it like compositions of functions.

Is $f(g(x))$ the same thing as $g(f(x))$? Hell nah!

In the question, it says T (R) is the transform U (P) followed by V (Q).

That is, the transform T takes some point $x$, you then put it through the function/transform "P" to get $P(x)$, this is the point. Now you take this new point and you put it in your new function/transform "Q" to get Q(P(x)). Just like function composition.

You then drop the brackets and remove the "x", of course, so: R = QP is P followed by Q.

Does that make sense? I can explain more if you'd like.

I am so sorry, but i still dont get it

If we have the function $f(x)$ and the function $g(x)$, how would you write down "f(x) composed with g(x)"?

hmm i dont know ... is it in C1 or C2 syllabus?

hmm i dont know ... is it in C1 or C2 syllabus?

I don't really know how to break it down in any simpler way ('cause I'm dumb). If you want a more systematic rule, you could just go:

QP is Q followed by P.
PQ is P followed by Q.

So in this question, UV = T, so i thought it would be PQ= R, because P represents U and Q represents V. But i know i am wrong?

No, in this question it's U followed by V. That is, U first and then V second.

And the second one comes first, (I know it's weird, but that's how it is):

So it's VU = T.

As to why the second one comes first, well, you'll need to re-read my first post.

Do you know what is this rule or topic called, so i can look it up on youtube?

This video explains it really well.

Thankyou for your time

I don't really know how to break it down in any simpler way ('cause I'm dumb). If you want a more systematic rule, you could just go:

QP is Q followed by P.
PQ is P followed by Q.

The video is really clear , and i think QP is not Q followed by P. It should be P followed by Q

Yep, you're right. That was me in my haze of tiredness, I'll correct it now - glad the video was useful.

yes thankyou for helping when u are tired, that was very helpful.