Practice Midterm #7
rsehrlich
Not completely sure, but I got T(a,b)=((7/2)a+(1/2)b, 2a). Did anyone else get this?
cwhiteside7: May 4, 2015, 3:17 p.m.
How did you get this?
nabihahshuaib: May 4, 2015, 3:59 p.m.
I got (3a+$\frac{5}{2}b, a+$\frac{1}{2}b)
nabihahshuaib: May 4, 2015, 4 p.m.
that didn't come out right. (3a+ (5/2)b, a+ (1/2)b)
nabihahshuaib: May 4, 2015, 4:02 p.m.
I found the identity matrix that maps the same points from gamma basis to beta basis. Then multiplied that matrix with the transformation matrix from basis beta to gamma. This would give the transformation equation just in the basis beta.
tanishaharlalka: May 4, 2015, 10:01 p.m.
I got that too @resehrlich
julianna_burke: May 4, 2015, 10:14 p.m.
Can you explain how you got this @tanishaharlalka and @rsehrlich
tanishaharlalka: May 4, 2015, 10:21 p.m.
Uhhh i first mapped the beta (1,1) basis to (1,0) and (1,-1) to (0,1). Then I multiplied both the basis times the T basis so I got (1, 3) and (1,2) respectively. Then I used those as my "directions" and used those as coefficients to multiply them to the gamma basis. Therefore, I got (4,2) and (3,2) respectively. Then in order to find T(1 0) and T ( 0 1 ) I used the beta basis and added them and subtracted them to manipulate it. For example, T( 1 1 ) + T( 1 -1 ) = T( 1 0 ) times one half. Afterwards, I plugged in the basis I got from gamma (4, 2) and (3,2) and plugged them in and got my answer. Sorry if this is confusing
tedallen: May 4, 2015, 11:48 p.m.
This was my solution http://i.imgur.com/SMfo2nH.jpg
julianna_burke: May 5, 2015, 12:23 a.m.
Thank you @tedallen
danielkim: May 5, 2015, 12:36 a.m.
This is how I did problem #7 https://www.camscanner.com/share/dtwLx/0/w105s0b1wpqzf
dannystapleton: May 5, 2015, 3:38 p.m.
@rsehrlich and @tanishaharlalka, I also got the same answer. Questions though, are theyre mutplie ways to write T(a,b)? I did it in vector form...
danielkim: May 5, 2015, 3:41 p.m.
I made a mistake in the link I posted. I got the same answer as @dannystapleton @rsehrlich and @tanishaharlalka https://www.camscanner.com/share/dtwLx/0/w105s0bjsxaol
rsehrlich: May 5, 2015, 3:58 p.m.
I believe that because T(a,b) is from R2->R2, we're supposed to write it as an ordered pair. Also, on another thread, someone said they asked a TA and they got the same answer I got.
brian_li: May 5, 2015, 11:43 p.m.
Is the given T taking beta to gamma, or gamma to beta?