Recent content by sphlanx

Homework Statement We are given a linear map f, f:R2xR2->R. f has the following properties: 1)It is linear for the changes of the first variable 2)It is linear for the changes of the second variable 3)f((3,8),(3,8))=13 We are asked to say if f is anyhow related to the normal inner...

Homework Statement Hello and thanks again to anyone who has replied my posts. Your help is a great deal and really appreciated. I have the following homework question which I have answered and I want a comment if it is valid or illogical: We are given a matrix, with eigenvalues 3 and...

Yes I think I got it now. The missing matrix is the matrix i posted on my first post. So T(x,y)=(2x+y,-5x+8y). The way you put it, I see that a matrix and a linear transformation are actually the exact same thing, expressed in a different way? Thank you very much, the work you people do here is...

Homework Statement Hello again. First of all thanks to anyone who has replied to my previous questions. Now, the question that troubles me is: We are given a matrix A2x2 with some random values and we are asked to say if there is a linear map which has A as its map for the standar basis...

Bump because deadline ends in 3 hours :) Thank you:P

Thanks about 1). About 2) the actual question is: "Is there a non-zero polyonymus that..??". It asks if it exists it doesn't say to prove that it exists. My bad. But are we sure that a non-zero polyonymus like the one in my original post doesn't exist?

Homework Statement We are given a linear map f:R2->R2 f(x,y)=(x,3x+8y). 1)prove that any linear map R2->R2, if it is 1-1(injective??) it is also...well i don't know the word! It is the property that every element of the destination set is imaged by the source set. (candidate is "surjective"...

Homework Statement We are given a subspace of R^3 that is produced by the elements: (2,6,2) abd (6,2,2). We are asked to find (if any) a homogeneous linear system that has this subspace as solution set. Homework Equations The Attempt at a Solution 1)The subspace is 2...

Homework Statement We are given a homogeneous system of 5 equations and 3 variables. We are asked to find the solutions (which i found to be unique and <0,0,0>) and then we are asked(along loads of other stuff:P): a)If any two linear transformations g and f have kerf=kerg=<0,0,0> then...

Homework Statement We have the following linear map: f:R^2-->R^3 f(x,y)=(x,3x+8y,x+y+11y) e is the standar basis of R^2 and a is the standar basis of R^3 Question: Is there a linear map g: R^3-->R^2 that the matrix of (fog, a,a) is the 0 matrix? Is there a linear map g...

Homework Statement First of all sorry if my terminology sounds a bit weird, i have never studied mathematics in english before. So this is the problem: We have the space R^2x2 of all the tables with numbers in R. We also have a subspace V of R^2x2 of all the tables with the following...