Advanced Higher Maths 2011-2012 : Discussion and Help

Hey all I've got some difficulty with one of the matrices question in a past paper question

SQA Past Paper 2007


It's question 5a only really, I'll take any inputs towards this question since I've tried looking over my notes, scholar and still don't know how to do it :/

Thank You

Sorry couldn't upload the question only because I'm on my iPad

Thank you my friend, you have cleared out my difficulties in solving matrices
And you from Glasgow what year in uni are you in and which high school did you come from ?

Haha no I'm just curious since I'm from Glasgow and also because he's in Cambridge

Finally understand complex equations!

Anyone know an actual use of complex numbers? We have just finished them and I can't seem to find a proper use for them. Ok so they let you find "non-real roots of polynomial equations". But doesn't that defeat the purpose of a root? Shouldn't it be where it crosses the x-axis i.e. when y=0. If it doesn't cross it then it doesn't have any roots not these "complex roots".

Anyone know an actual use of complex numbers? We have just finished them and I can't seem to find a proper use for them. Ok so they let you find "non-real roots of polynomial equations". But doesn't that defeat the purpose of a root? Shouldn't it be where it crosses the x-axis i.e. when y=0. If it doesn't cross it then it doesn't have any roots not these "complex roots".

Essentially the complex numbers are just an extension of our number system. Have you heard of diophantine equations? They're equations where solutions can only be integers, eg 3x=2 has no solutions. Or in the past, before negative numbers were considered ok the equation x+1=0 would be considered insoluble.
Equally, when we only have rationals(fractions), we would say the equation x^2=2 is insoluble. Moving from the positive integers, to all integers, to rationals to reals is just adding to the number of polynomials we can totally solve.
In adding the complex numbers, we get to a complete field, that is every polynomial of degree n will now have n roots. That's basically the point of them, and leads onto the Fundamental Theorem of Algebra.

Well, we've only had one lesson on them, but our teacher mentioned in passing that the maths of complex numbers underlies a lot of physics about electricity. Don't ask me how :L

The whole point of having a new number system is that the solutions are a different thing, but still useful. When negative integers were first used, people might have questioned the value of a solution to x+4=3, since from a counting point of view you can't have -1 apples. But negative integers have their uses both in maths and the sciences, and the same is true of complex numbers - even if a complex solution isn't quite the same thing as a real solution.

I think the problem is that we have been introduced to complex numbers and taught no real-world applications for them.

Anyone know an actual use of complex numbers? We have just finished them and I can't seem to find a proper use for them. Ok so they let you find "non-real roots of polynomial equations". But doesn't that defeat the purpose of a root? Shouldn't it be where it crosses the x-axis i.e. when y=0. If it doesn't cross it then it doesn't have any roots not these "complex roots".

Anyone know an actual use of complex numbers? We have just finished them and I can't seem to find a proper use for them. Ok so they let you find "non-real roots of polynomial equations". But doesn't that defeat the purpose of a root? Shouldn't it be where it crosses the x-axis i.e. when y=0. If it doesn't cross it then it doesn't have any roots not these "complex roots".