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a) express α1 in the form α1=b1β1 + b2β2 and find an expression for α2

seems like you need to find a vector that satisfies D....hmm

the answer for \[\alpha _{1}=2\beta _{1}+3\beta _{2}\]

though I don't know how to get to the answer

Can anyone help me out?

so is this a set?

yup D and E (which are really S and T) are two sets or basis for the plane

how would you construct the matrix?
so that I can eliminate
\[\alpha _{2}\]

sorry, basis and s-coordinates are still really shaky for me

ok here
its simple...you dont need matrix

ok here
its simple...you dont need matrix

oh awesome, ok thanks a lot! I'm guessing for \[\alpha _{2}\] we eliminate (alpha)1

yeah exact same way...sets are usually simple to solve if you know the algebra "tricks"

you dont need a lot to solve them i mean...they seem difficult but it usually is very easy

nvm, i think i got it, A[-1/2A^2+7/2A-1/2IN]=In....where [] equal A^-1?

yeah if you find the correct inverse...
check to be sure that that matrix is infact an inverse

How would you do that? A isn't defined

hmmm....its trivial...you let it be arbitrary...look at the determinant for such arbitrary A

So let A be 2x2 matrix [a,b][c,d] and solve?

you can. if its nonzero then A is non-singular

you just plug them in to your answers from i), sorry

yeah you can use either system used to solve to find the T coord.

this is hard but im here to help