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Linear transformation representation with a matrix
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[QUOTE="patricio2626, post: 5477814, member: 594622"] [h2]Homework Statement [/h2] [I]For the linear transformation T: R2-->R2 defined by T(x1, X2) = (x[SUB]1[/SUB] + x[SUB]2[/SUB], 2x[SUB]1[/SUB] - x[SUB]2[/SUB]), use the matrix A to find T(v), where v = (2, 1). B = {(1, 2), (-1, 1)} and B' = {(1, 0), (0, 1)}.[/I][h2]Homework Equations[/h2] T(v) is given, (x[SUB]1[/SUB]+x[SUB]2[/SUB], 2x[SUB]1[/SUB]-x[SUB]2[/SUB]) [h2]The Attempt at a Solution[/h2] Okay, I see that T(v) is simply (2+1, 2*2-1) --> (3, 3), but this matrix business has me a bit confused. From my textbook: [I]Using the basis B = {(1, 2), (-1, 1)}, you find that v = (2, 1) = 1(1, 2) - 1(-1, 1), which implies [v][SUB]B[/SUB] = [1 -1][SUP]T[/SUP].[/I] Now, where did this seemingly 'magical' 1 and -1 come from? The matrix relative to B and B' is obviously {(3, 0), (0, 3)}, but I have no idea where this [1 -1][SUP]T[/SUP] came from, nor what it is. I see that this is the coordinate matrix for (3, 3) relative to B, because I see that A*v in this case gives (3, 3), but have no idea how it was derived. Perhaps there's some small gem or concept here that I'm missing? [/QUOTE]
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Linear transformation representation with a matrix
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