Advanced Higher Maths 2012-2013 : Discussion and Help Thread

I was wondering if anyone could give me a bit of help with some homework questions I have.

First one is Gaussian Elimination. I have worked it out to be redundant however the answers at the back say that it is solveable. I was wondering if someone could point out where I went wrong or if the answers are.

Q)3x + 2y +5z = 0
2x + y - 2z = 5
7x + 4y + z = 10

3 2 5 | 0
2 1 -2 | 5
7 4 1 | 10

R2 =3R2 -2R1
R3 = 3R3 -7R1

3 2 5 | 0
0 -1 -16 | 15
0 -2 -32 | 30

R2 = 2R2

3 2 5 | 0
0 -2 -32 | 30
0 -2 -32 | 30

R3 = R3 - R2


3 2 5 | 0
0 -2 -32 | 30
0 0 0 | 0

Row of 0's = Redundant therefore infinite solutions , given in terms of K.

So I have given my answers as z =k etc but the back says the answer is x=1, y= 1, z=-1.

So where is the mistake? Thanks

I was wondering if anyone could give me a bit of help with some homework questions I have.

First one is Gaussian Elimination. I have worked it out to be redundant however the answers at the back say that it is solveable. I was wondering if someone could point out where I went wrong or if the answers are.

Q)3x + 2y +5z = 0
2x + y - 2z = 5
7x + 4y + z = 10

3 2 5 | 0
2 1 -2 | 5
7 4 1 | 10

R2 =3R2 -2R1
R3 = 3R3 -7R1

3 2 5 | 0
0 -1 -16 | 15
0 -2 -32 | 30

R2 = 2R2

3 2 5 | 0
0 -2 -32 | 30
0 -2 -32 | 30

R3 = R3 - R2


3 2 5 | 0
0 -2 -32 | 30
0 0 0 | 0

Row of 0's = Redundant therefore infinite solutions , given in terms of K.

So I have given my answers as z =k etc but the back says the answer is x=1, y= 1, z=-1.

So where is the mistake? Thanks

I see no mistakes in your working.

There is no mistake. I think the book just set k to a particular value (probably z = k = 1) and had that as the canonical solution.

Note that redundant and solvable are not mutually exclusive. Redundant just means it's solvable with infinite solutions. Redundant and uniquely solvable are exclusive, and so are inconsistent and solvable.

hi can some one tell me if these answers are correct:
Q:differentiate x/(1-2x)
A:2x-2

Q:differentiate x^2/(x^2+1)
A:1/(x^4+1)

Q:differentiate x(x-1)^(1/2)
A: (3/2)x-1

Question 1, nope, you should be using the quotient rule here!

Question 2, quotient rule again, wrong answer

Question 3, product rule here, wrong answer

Quotient rule:
$if \ f(x) = \frac{g(x)}{h(x)} \Rightarrow f'(x) = \frac{g'(x)h(x) - g(x)h'(x)}{h^2(x)}$

Product rule:
$if \ f(x) = g(x)h(x) \Rightarrow f'(x) = g'(x)h(x) + g(x)h'(x)$

Solutions

Question 1:


Question 2:


Question 3:

I was wondering if someone could help me with this question:

n + n = 28
1. 2

I don't understand what I have to do to solve the problem

It means that you must find n such that the equation

$\displaystyle\binom{n}{1} + \displaystyle\binom{n}{2} = 28$

is true.

Perhaps you should try using the fact that

$\displaystyle\binom{n}{1} + \displaystyle\binom{n}{2} = \displaystyle\binom{n+1}{2}$

And then equating the RHS with 28. Afterwards try expanding the binomial coefficient into its factorial definition.

It means that you must find n such that the equation

$\displaystyle\binom{n}{1} + \displaystyle\binom{n}{2} = 28$

is true.

Perhaps you should try using the fact that

$\displaystyle\binom{n}{1} + \displaystyle\binom{n}{2} = \displaystyle\binom{n+1}{2}$

And then equating the RHS with 28. Afterwards try expanding the binomial coefficient into its factorial definition.

I've seen you do this question so many times in the last year I can do it as soon as I see it now. I didn't even encounter it when I did AH. Got it in one past paper.

I don't think I actually ever did a question like this for real when I sat AH Maths

God that was a long time ago... Time flies like an arrow, fruit flies like a banana.

Last year at Cambridge...I wish you the best of luck. Still planning on PhDing? In category theory?

Thanks Yes and yes, although now I'm slightly regretting declining Yale and Columbia.

Correction: Ivy League + no tuition fees + $1500 stipend per month + opportunity to teach undergrads of said Ivy League for more stipend

Correction: Ivy League + no tuition fees + $1500 stipend per month + opportunity to teach undergrads of said Ivy League for more stipend