Excellent! This has been omitted from the Edexcel textbook. Whoever wrote that chapter should be ashamed of themselves. Should not have been allowed without further revisions to the text.
@ALevelMathsRevision4 жыл бұрын
Yes the textbook does seem to be lacking on this front.
@vladid58962 жыл бұрын
Great video, but I think you might have gone the hard way to find the invariant lines of your matrices. Taking your (7 24 | 24 -7) matrix, you can make the problem much more simple by comparing coefficients. At the stage where you have 24x - 7mx - 7c = 7mx + 24m2x + 24mc + c, you can approach it differently: without taking the terms to one side, by grouping the x terms and the c terms as follows: (24 - 7m)x - 7c = (7m + 24m2)x + (24m +1)c ; you can compare coefficients. This gives you 2 equations; (1.) 24 - 7m = 7m +24m2 24m2 + 14m - 24 = 0 (Taking the terms to one side) m = 3/4 or -4/3 (Done by quadratic formula) and (2.) -7c = (24m + 1)c (24m + 8)c = 0 (Taking the terms to one side) c = 0 (ignoring 24m + 8 = 0 as m is shown NOT to equal -1/3 in equation (1.)) Hence invariant lines are: y = 3/4 x y = -4/3 x I personally find this easier, but this might not be the case for everyone. I hope this helps.
@ALevelMathsRevision2 жыл бұрын
Thank you for the alternative take on things. I'm sure lots of people will find it useful.
@kazishahjalal6852 Жыл бұрын
Your method is great but clearly it doesn't explain why m is not equal to -1/3. You can put m=3/4 and -4/3 in equation 2 and still find they are not equal. Thanks for sharing your method though.
@himanshu7544 Жыл бұрын
Lifesaver
@awall0072 жыл бұрын
When you plug in x=0 and m=-1/3 to y=mx + c then you get y = c where x = 0 and c is free. Why does this imply only the origin is invariant instead of the y axis being invariant?
@melodyzhang69696 ай бұрын
What happens if the question asks you to find the invariant line but with a condition of c is not 0?
@melodyzhang69696 ай бұрын
Nvm I figured it out
@richardvolkov48672 жыл бұрын
thanks
@ALevelMathsRevision2 жыл бұрын
Glad to help
@clement_jacob3 жыл бұрын
hmm not sure about this, you said you need to prove y prime = x prime + c, but you used this statement in your proof itself. Isnt this counter intuitve your proofing something by using itself in the actual proof.
@ALevelMathsRevision3 жыл бұрын
The chain of implications certainly holds and it scores full marks in an exam.
@clement_jacob3 жыл бұрын
@@ALevelMathsRevision ok ty for the comment 👍😁. if I instead chose to find the invariant lines normally in that situation would I still score top marks?
@ALevelMathsRevision3 жыл бұрын
@@clement_jacob what do you mean by "normally"? Any valid method scores full marks.
@ALevelMathsRevision3 жыл бұрын
Also, keep arguing to the death. It's what makes a good mathematician 🙂
@clement_jacob3 жыл бұрын
@@ALevelMathsRevision as in like you know how you solved it in the second example, if I attempted and solved the question one in this video just like you solved questions 2 I would get all marks right ? ty for helpful comments btw I appreciate it