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Unformatted text preview: god/Q7Wawi MATH 323501, 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.) +(ﬂﬂjb
,:HZ*KW%,.
Klrak; 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’4cj :_ 0’54“ {*Xél—(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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 Fall '08
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 Linear Algebra, Algebra, Linear map, linear transformation, Homomorphism, ROW __________ _~

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