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anonymous
 5 years ago
Let D={α1,α2} and E={β1,β2} be two bases for the plane, and suppose that β1=5(α1)3(α2) and β2=3(α1) + 2(α2)
anonymous
 5 years ago
Let D={α1,α2} and E={β1,β2} be two bases for the plane, and suppose that β1=5(α1)3(α2) and β2=3(α1) + 2(α2)

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anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0a) express α1 in the form α1=b1β1 + b2β2 and find an expression for α2

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0seems like you need to find a vector that satisfies D....hmm

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0are you getting \[\alpha1 = b1\left[ 5(a1)  3(a2) \right] + b2\left[ 3(a1)+2(a2) \right]\]? Then for \[\alpha2\] it might be similar

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0the answer for \[\alpha _{1}=2\beta _{1}+3\beta _{2}\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0though I don't know how to get to the answer

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0\[\alpha _{2}=3\beta _{1}+5\beta _{2}\] I have a difficult time understanding most of basis and Scoordinates

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Can anyone help me out?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0yup D and E (which are really S and T) are two sets or basis for the plane

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0how would you construct the matrix? so that I can eliminate \[\alpha _{2}\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0sorry, basis and scoordinates are still really shaky for me

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0ok here its simple...you dont need matrix

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0ok here its simple...you dont need matrix

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0\[\beta_{1}= 5\alpha_{1}  3\alpha_{2}\] (1) \[\beta_{2}= 3\alpha_{1} + 2\alpha_{2}\] (2) if you multiply (1) by 2, and if you multiply (2) by 3 you get \[\2beta_{1}= 10\alpha_{1}  6\alpha_{2}\] \[\3beta_{2}= 9\alpha_{1} + 6\alpha_{2}\] adding the above two equations, you eliminate the parameter \[\alpha_{2}\] and it becomes \[\2beta_{1} + \3beta_{2}= \alpha_{1} \]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0oh awesome, ok thanks a lot! I'm guessing for \[\alpha _{2}\] we eliminate (alpha)1

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0yeah exact same way...sets are usually simple to solve if you know the algebra "tricks"

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0you dont need a lot to solve them i mean...they seem difficult but it usually is very easy

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0cool, hey since I have you here would you know how to conclude that A is nonsingular given the equation \[In=1/2[A ^{2}7A+In]A\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0nvm, i think i got it, A[1/2A^2+7/2A1/2IN]=In....where [] equal A^1?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0yeah if you find the correct inverse... check to be sure that that matrix is infact an inverse

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0How would you do that? A isn't defined

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0hmmm....its trivial...you let it be arbitrary...look at the determinant for such arbitrary A

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0So let A be 2x2 matrix [a,b][c,d] and solve?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0you can. if its nonzero then A is nonsingular

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0K thanks, going back to the basis question, if the S coordinates of point P are (9, 3), what are it's T coordinates?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0you just plug them in to your answers from i), sorry

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0yeah you can use either system used to solve to find the T coord.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0this is hard but im here to help
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