solutions_501_07 - god/Q7Wawi MATH 323-501 QUIZ 7 Fall...

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Unformatted text preview: god/Q7Wawi MATH 323-501, QUIZ 7. Fall 2.010 NAME_________‘___.._ ROW __________ _~ Show all steps for credit. Q1. (3 pts.) Define L 1: R2 —> R2 by f 15K )) = ( '31:; ) Deterrfiine whether L is a linear transformatién. . g ' x, , Lsm _ (hpr 1+7}, Lf(><;§+ (34).," (Ya—x2.) +(flfl-jb ,:HZ*KW%,. Kl-rak; 1" U‘Tfla L( Yr“?! (4, k‘r'fl, x . P L I +L( L31 h a») xlfijfikfia) (m) :1; 'AJb’r A (Emu /’\ Q2. (3 pts.) Define a linear transformation L : P3 —-> R2 by Lane» = (132(3) ) - Find the kernel of L. ' (O L( +Lk+c> GF‘L“ +C 4+L+c:o .r l (9 gz‘zl‘mo) pa Jo +930 (9“ ( ‘3 'L" a _—.=>' Lao/V4,..-c [zr’ék‘z’4-cj :_ 0’54“ {*Xé-l—(E. _> Q3, pts) lf L1, L2 : V ——r W are linear transformations and L : V ——> W is defined by I I A ' ' L(v) = L1('U) + L201), '11 E V, prove that L is a linear transformation. L(U+u\ > L.(V+u> + 1,1614%:- A61} 4—L‘Cu) +LL(\/)+L&(\43 : L.(vl4~LL(v\ +L.(w\’r(fa(w\ : L(v) +L{~J§. / ...
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