Recent content by b00tofuu

Let F= R or C, and A = [1 2 3] is considered as linear operator in F3 [0 1 2] [0 0 1] then the minimal polynomial of A = (x-1)^3, can we say that the primary decomposition thm doesn't give any decomposition, can we find an invertible P s.t P^-1*A*p is a block diagonal matrix?

no, it's not what i meant... its the squared of the inverse function of (x^3+x^5). a.the question first asked about the volume of solid revolution of a function y=f(x) bounded by y=b, and the y axis. the function crossed (0,0),(a,b) where a>0. i'vc got the answer int(phi(f(y)^-1)^2, y = 0 ...

Homework Statement let f(x)=x^3+x^5. Evaluate int((f(x)^-1)^2, x = 0 .. 2) The Attempt at a Solution i have a feeling that it has a relation with counting volume of a solid revolution.but i don't know how to answer it...

thank u... i understand problem 1 now...for problem 2, I'm sorry. you're right, it's from 0 to t not 1... thank u...

Homework Statement problem 1 diff([f(tanx)], x) = x^2; prove that diff[f(u)]=(tan^-1(u))^2/(1+u^2) problem 2 int(f(u), u = 0 .. 1) = f(t)-1; prove that f(a+b)=f(a)f(b) for every a,b ∈R The Attempt at a Solution problem 1 i don't know how to answer this...

the zero point

a point...? but i still don't understand how to write the proof... T_T

its the number of vector in any basis for a subspace

let U and V be subspaces of Rn. Prove that dim(U+V)=dim U+dim V - dim(U∩V)

thank u, i got it now...

suppose v1,...,vk are nonzero vectors with the property that vi.vj=0 whenever i is not equal to j. Prove that {v1,...,vk} is linearly independent.