Recent content by misterau

I need to show that f(x,y) = x/y has a right inverse that is a function f-1: R → R2 \ { (x,0) |x ∈ R} so that f . f-1(x) = x

Homework Statement I'm wondering how to find the inverse function of some f(x,y)? Homework Equations The Attempt at a Solution

Homework Statement http://img40.imageshack.us/img40/6421/57065635.jpg The Attempt at a Solution I just what to know what the hollow I symbol is? Is it just 1 0 0 0 1 0 0 0 1 Thank you!

Homework Statement Show that the distance D from the origin of any point (x , y , z) lying on the plane x + y + z= 1 satisfies D^2 + x^2 + y^2 +(x + y -1)^2 . By considering partial derivatives, find the point that is closest to the origin. Prove that this distance is genuinely minimal...

Homework Statement A = -10 6 3 -26 16 8 16 -10 -5 B = 0 -6 -16 0 17 45 0 -6 -16 (a) Show that 0, -1 and 2 are eigenvalues both of A and of B . (b) Find invertible matrices P and Q so that (P^-1)*(A)*(P) = (Q^-1)*(B)*(Q)= 0 0 0 0 -1 0 0 0 2 (c) Find an invertible...

Homework Statement Is there a basis of R4 consisting of eigenvectors for A matrix? If so, is the matrix A diagonalisable? Diagonalise A, if this is possible. If A is not diagonalisable because some eigenvalues are complex, then find a 'block' diagonalisation of A, involving a 2 × 2 block...

Oh yeah didn't think of that!:smile: Thanks!

Homework Statement Let the function f be given by f (x) = x^2 (a) Determine the tangent line to the graph of f at x = 1. Denote this by y = g (x) . (b) Let \epsilon be a positive number. Solve the inequality|f (x) - g (x)| <\epsilon (c) What does part b) tell us about the accuracy of the...

nvm I worked it out. Thanks for the help.

I am not understanding how this helps me do the problem? If you could show me an example or link to an example I would be thankful.

Homework Statement f(x , y) = y^3 + x^3 Calculate the partial derivatives fx and fy and show they are continuous at each point (x,y) ∈ R^2 Homework Equations A function is continuous on a region R in the xy-plane if it is continuous at each point in R A function f is continuous at...

Homework Statement The real valued function f of two variables is defined by f(x,y) = tan( (1/2) *(pi) *sqrt( (x^2 + y^2) )/( sqrt( (x^2 + y^2) ) for each (x,y) satisfying 0 < x^2 + y^2 < 1. How should f(0,0) defined so that f is continuous at (0,0)? Homework Equations The Attempt at a...

I really not sure, probably not correct... x != c1*v + c2*w x = c1*v + c2*w + c3*u u = c1*v + c2*w + c4*x c1*v + c2*w != c1*v + c2*w + c3*u 0 != c3*(c1*v + c2*w + c4*x) 0 != c1*v + c2*w + c4*x

Homework Statement Suppose that u, v, w and x are vectors in a vector space V . If x !∈ span(v,w) and x ∈ span(u, v,w), does it follow that u ∈ span(x, v,w)? Justify your answer. Homework Equations The Attempt at a Solution Not really sure how to even start this problem. Any hints would be...

To span a space means that every vector in the space can be written as a linear combination in the set.