Recent content by Kraz

I figured it out. I have one last questions if I may ask: Lets say you have 2 other vectors which are part of set T, these 2 vectors g1 and g2 can be expressed in terns of the vectors in a set of a basis called S. By considering the 2 × 2 matrix A = ((g1)S(g2)S) whose columns are the...

well because f1(x)= 1 , f2(x)=x, so v=af1 + bf2 , where v=f1 1= a+bx, so for every x and every value of A,B the coordinates are (a= 1-bx , b=b)

Yes I understood, I did not really know that it must be valid for all x, which was a dumb mistake as I should have realized that by looking at this equation: (Af1+Bf2)(x)=0is it then correct to say then that the coordinate (f1)s with respect to the basis S is the follwoing column matrix ...

thanks, but let's say we have a set of vectors (v1,v2,v3...vn) do you agree that if this set is dependent Av1+Bv2+Cv3...=0, then A could have different values that lead to the solution, obviously each time A changes the other sclars change to?

yes but if I put a different x, there will always be different values of A and B such that that equation would equal 0, therefore. could you maybe ellaborate your logic? Thanks Do you mean that in order for the set to be not independent I would need to find a function h(x) with specific...

what do you mean, I am not english so do not really understand, but as x is elemnt of R it can take any of such values, and so can the scalars, as g(x)=0, A+Bx=g(x) for example when A=2, B=2 and x=-1 ... and many more

Hello, I am just doing my homework and I believe that there is a fault in the problem set. Consider the set of functions defined by V= f : R → R such that f(x) = a + bx for some a, b ∈ R It is given that V is a vector space under the standard operations of pointwise addition and scalar...