Recent content by leej72

Sorry I misread your problem, since there are no common elements in each vector, there is no dimension for the intersection of S and T because they have no common elements

When I said approaching from the limit x = y^3, I meant from the path.

Approaching from the limit x = y^3, we get lim = y^3/ 2(y^3) (x,y) -> (0,0) = 1/2 Since the value of the limit from the path x = y^3 is not equal to 0 (the value that you have been getting), then the limit does not exist

Well in this case it would be the rows that both S and T have common elements in. Hint: look past the parameters s,t

Yes that was a typo, I did mean from 0 to 9 but I am not too sure if the first number would be allowed to be a 0. I would personally think otherwise, not letting the first number to 0

You are on the right track, think about it this way. You have a choice of choosing the numbers from 1 to 9 and then you have three cases: 1. the case where all 4 numbers are the same number as you chose 2. the case where 3 numbers are the same number as you chose as well as you have to...

Yes, the dimension for those matrices are 2, when talking about dimension we either talk about row or column dimension. the S ∩ T means all the elements that are common in S and T.

Thanks a lot for helping me out, I guess I was overcomplicating the question because we are covering different topics, mainly Gram-Schmidt process so I thought we would have to incorporate that into the question.

I attached the pdf file of the question, it is question #1b.

Homework Statement Let u1 = [1 1]^T and u2 = [0 -1]^T. Find a 2 x 2 real matrix A so that the function T_A is a map from ℝ^2 to ℝ^2, given by multiplication by A, T_A := Av, sends T_A(u1) = v1 and T_A(u2) = v2 where v1 = [cosθ sinθ]^T and v2 = [-sinθ cosθ]^T. Explain/justify your...

Homework Statement Give a genuinely new (i.e. not discussed in class or in the book or in tutorial) example of: two sets X and Y , and two functions f : X →Y and g : Y → X, such that the composition g ◦ f is the identity function 1X : X → X, but neither f nor g are bijective. (Reminders: if...