MA 35100 Lecture Notes - Lecture 34: Linear Map, Parallelogram, If And Only If
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Linear transforth from rectors to rectors (t:#w-aw) Find a matrix representing 7, i. e. amen, with t = ta where ta(x): ax ex: t: rer2, t [y]=(2"j3] Find a matrix representing the linear transformation that transforms one parallelogram into another. Matrix for a linear transforth ta: av-hm where 14, rw have bases. Matrix for linear transfrnthc:u-2 where v, we have bases band b. ex: let t:py "py be the 1t given by thy)=y"+xy with respect to basis. B = 31,1+x, x2, x33 for ps and b = 31+x, x + x3,x"+x3, x43 for py. Goal: work out what i does to the elements of b. 1c17x) + 0(x+x2) +1(x") + 0x3 + 0x. ~> o(1x) + 2(x + x2)-2(x2) = 12x3) - 8x4. Ta: r" rm, a is myn aimpy x dim py i. e. 5 x l ex: find the matrix representing the lt given by multiplication by a: (ii3) with respect tob = 5(2], [173 and b =3 (1), (3)3.
