Let A = [ali ] be a given /II x I! matrix. and let V and IV be given vector spaces of dimensions II and /II, respeclively. LeI S = iVI. V, ..... 'n} be an ordered basis for V. and let T = (W I. ""2 .. .. . w"') be an ordered basis forIV. Define a function L : V -4 IV by. L(v;) = L al;w . i = 1.2 ..... 11.I=jand if ll: = (. j VI + Cl V, + ... + Cn V", we deline L(x) byL(x) = L c,L(Vi).;=1(a) Show that L is a linear transformation.(b) Show that A replesents L with respect to Sand T.

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