WACE Stuff > Mathematics Stage 3
Maths 3A/3B
anotherworld2b:
I'll ask about q21 if i have any more queries about it. :)
I was wondering for q15 am I doing something wrong? Because im getting the wrong answers for x and y so far. Also for q17 how do I prove generally?
--- Quote from: jamonwindeyer on September 06, 2016, 01:25:25 am ---Where are you up to with Q21? Have you started by multiplying the vector I suggested above with the matrix given? That will apply the linear transformation, did you get that or is that operation troubling you? :)
Question 15 isn't really attackable with the method you used, you are better off using simultaneous!
Using the statement given, we conclude the following:
Do a similar thing for the multiplication of BA (the other way around), then you'll have four sets of simultaneous equations. Solve each to obtain an answer ;D
For Q16 ,you have the right idea, but remember that matrix multiplication is not commutative! That is:
When you factored, you put the P out the front, it should have been out the back to preserve the initial order of the matrices, try again with:
Question 21 is asking you to consider general vectors and do a general proof of the statements given, kind of like a standard algebraic proof! :) so, consider A and B as non-singular (invertible) square matrices where \(AB=BA\), and prove generally that:
Let me know how you go! ;D
--- End quote ---
jamonwindeyer:
--- Quote from: anotherworld2b on September 06, 2016, 11:27:06 pm ---I'll ask about q21 if i have any more queries about it. :)
I was wondering for q15 am I doing something wrong? Because im getting the wrong answers for x and y so far. Also for q17 how do I prove generally?
--- End quote ---
Hmm, I don't see any errors in your working immediately, what are the answers supposed to be? :)
An example for 17a) to show you a general proof:
At no stage do I specify what A or B should be, I've proved it generally!
anotherworld2b:
The answers for q15 are:
X= -1 , y= -2 , p= -5 , q= 7 , r= -7 , s=2 but now sure why.
Oh okay I get how to do q17 now thank you ;D
I also want to ask for q13 what would be the best way to do it?
I also tried q14 but i also got the answer wrong for some reason
--- Quote from: jamonwindeyer on September 07, 2016, 12:07:03 am ---Hmm, I don't see any errors in your working immediately, what are the answers supposed to be? :)
An example for 17a) to show you a general proof:
At no stage do I specify what A or B should be, I've proved it generally!
--- End quote ---
anotherworld2b:
I was also wondering if i can get help with these two questions. Particularly q13
jamonwindeyer:
--- Quote from: anotherworld2b on September 07, 2016, 12:21:31 am ---The answers for q15 are:
X= -1 , y= -2 , p= -5 , q= 7 , r= -7 , s=2 but now sure why.
Oh okay I get how to do q17 now thank you ;D
I also want to ask for q13 what would be the best way to do it?
I also tried q14 but i also got the answer wrong for some reason
--- End quote ---
Oh! The matrix I gave you in my original explanation had a sign error for Q15, dictation error, sorry! Go back and look at your first line of working, do the matrix multiplication again, fix the sign errors and repeat, your method is 100% correct ;D
Question 13, best way to do it would (I think) just be considering a general matrix \(\begin{bmatrix}a & b\\c &d\end{bmatrix}\) and setting up simultaneous equations just like above!
Question 14, your attempt isn't quite correct. To make it clearer, try drawing a little diagram!
Triangle 1 ------ (Matrix A) -------> Triangle 2
Triangle 1 ------ (Matrix B) -------> Triangle 3
The idea here is to go from Triangle 2 to Triangle 3. We can do this by going back to Triangle 1, then to triangle 3, the matrix therefore being:
where A is the first matrix given, B is the second matrix given :)
Have you seen this method before? If not happy to explain! :)
--- Quote from: anotherworld2b on September 07, 2016, 10:15:25 pm ---I was also wondering if i can get help with these two questions. Particularly q13
--- End quote ---
Question 12 should be fairly straightforward, calculate the inverse:
Then multiply it by itself, form 4 equations and then solve for the missing variables! Show me your working if that doesn't quite work! :P
Then Q13 I addressed above ;D
Hope this helps!! ;D
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