Recent content by vcb003104

Hey guys, So, I was in my materials lecture today and something the lecturers and the tutors said was slightly confusing. We were talking about the repulsion and attraction force between atoms. This is all good as I can understand how if two atoms will repel each other if they get really close...

Yep , so I found that since a + b + c + d= 0 3a + 2b + c = 0 c = -(3a + 2b) d = -(a + b - 3a - 2b) = 2a + b P(x) = [itex] ax^3 + bx^2 - (3a + 2b)x + (2a + b) like this? but may I ask why do we need to eliminate c and d and g and h? Is so that it looks 'neater' or actually...

Right, so like: p(1) = a + b + c + d = 0 p'(1) = 3a + 2b + c = 0 →c = -(3a + 2b) ∴ p(x) = ax^3 + bx^2 -(3a + 2b)x + d let f and g be an element in S where f(x) = ax^3 + bx^2 -(3a + 2b)x + d and g(X) = ex^3 + fx^2 -(3e + 2f)x + h f(x) + g(x) = ax^3 + bx^2 -(3a + 2b)x +...

So if f(1) = 0 that's a + b + c + d = 0 f'(x) = 0 that's 3a + 2b + c = 0 right and g(1) = 0 that's e + f + g + h=0 g'(1) = 0 is 3e + 2f + g = 0 wouldn't (f + g)(1) just be a + b + c + d + e + f +g + h = 0? and (f + g)'(1) be 3(a + e) + 2(b + f) + (c + g) = 0?

Hi there, but how can I say that f and g is part of s? p(1) and p'(1) are both in S right? so aren't they something like ax^3 + bx^2 + cx + d = 0 ? because S = {p∈P3|p(1)=0,p'(1) = 0} so since p(1) = 0 does it mean that it is non empty?

Can I show f+g by saying that: (f+g)(x) = ax^3 + bx^2 + cx + d + ex^3 + fx^2 + gx + h = (a + e)x^3 + (b + f)x^2 + (c + g)x + (d + h) =f(x) + g(x) (Do I need to do the same for f'(x) and g'(x) kf(x) = k(ax^3 + bx^2 + cx d) = akx^3 +bkx^2 + ckx + d =(kf)(x) (Do I need to...

Hi there, but how do I find the ones that have more than one way of writing it? Do I solve the matrices for 3+ 2r= x+ y+ zr^2, 5+ 12r= x+ 4y+ z, and 2r= y+ zr^2 and make it to have a free parameter so that there are infinite solutions?

So my part b is alright? In the first part I want to say something like f(x) is in S and g(x) is in S To show that S is a subspace I need to show that (f+g)(x) is in S and kf(x) is in S right?

Homework Statement let r be an element of R ... 1.... 1 ......r^2.....3 + 2r u =( 1 )...v = ( 4 )...w = (1 )...b = ( 5 + 12r) ...0.....1......r^2 ...... 2r (sorry don't know how to type matrices) 1. For which values of r is the set {u, v, w} linearly independent? 2. For which...

Hi there, I was thinking if I can prove the u+v is an element of S like this: f(x) = ax^3 + bx^2 + cx + d = 0 g(x)= ex^3 + fx^2 + gx + h = 0 (f+g)(x) = ax^3 + bx^2 + cx + d + ex^3 + fx^2 + gx + h = (a+e)x^3 + (b+f)x^2 + (c+g)x + (d+h) = 0 and to show that Ku is an...

So that is the additional of functions right? How about multiplication? is it included in the equation as well?

So I can just expand it? Can I say, showing that this is a vector space via the addition of functions: sin(x)(af+ bg)''+ x^2(af+ bg)= 0 LHS = sin(x)(af+ bg)''+ x^{2}(af+ bg) = sin(x)(af)"+sin(x)(bg)" + x^{2} (af) + x^{2} (bg) = sin(x)af"(x) + x^{2}af(x) + sin(x) bg"(x) +...

Oops yep I meant subspace haha So d = 0 3a + 2b + c = 0 So p(x) = ax^{3}+ bx^{2}+cx

Hi there, Thanks for the reply, So to show f(x) and g(x) both satisfy the equation, do I just write sin(x)f"(x)+x^{2}f(x)=0 sin(x)g"(x)+x^{2}g(X)=0 Thus af(x) + bg(x) =a[sin(x)f"(x)+x^{2}f(x)] + b[sin(x)g"(x)+x^{2}g(X)] =a(0) +b(0) =0 Sorry I'm a bit slow at this

Hi but how can I answer the first question? determine if S is a subspace of P3? They didn't give me any equations or anything. There is only p(1) = 0 and p'(1) = 0