108APracticeQuizG - Name Wm Mathematics 108A Practice Quiz...

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Unformatted text preview: Name: Wm Mathematics 108A: Practice Quiz G May 3, 2010 Professor J. Douglas Moore Part I. TrueaFaise. Circle the best answer to each of the following questions 1‘ The m x n matrix A E menGR) defines a linear map L; :R“ —-> 132’” by LAX) : Ax. The nuil space of this linear map is the space of solutions to the homogeneous linear system £11231 +a12$2+ ‘ "§*Gln$n m 0, 02:51:14” 022% + ""i' aenmn fl 0. ‘ (1) 0 ll (1:113:51 'l' (11112352 ”I“ ' 'l' amnzn TRUE FALSE 2“ The range of the linear map LA is the space of vectors b m (b1, ‘ . .,bm) in Rm such that the linear system €131I1+812$2+"'+€1:n$n =3 51: 321$1~l~ {122132 '1" ' ' ' + G2n$n = 52: anal-731 + 3:112:32 “l“ “l” amnxn W firm has a solution, 3‘ According to one of the Main Theorems of Chapter 2 £11 the text, d§m(N(LA)) «+— dimmwm : ml /r~"-~‘""—-«=. TRUE FALSE) .m—d’ 4‘ Suppose that m «~_»~ n. Then the nonhornogeneous linear system 011$1 'i" (112% +‘ ~+ (1111227: '~”—'" 51. £12111 + @2532 + ' * '- + Gamma = 52. (1:11:31 ”i” 3222-712 + ' ‘+ 311113511 = bm has a solution for any choice of ((31, b2, . 4.5“) if and only if the corresponding homogeneous linear system {113$} 'i' 012% + ‘ ' '- + Emma = 0, #32332 + deems "i” " + aznfltn a 0: 07111131 "i“ aneie "i“ '+ annrn == 0 has no solutions FALSE Part II. Muitipie Choice. Circle the best answer to each of the following questions" 5. Suppose that L A : R5 —+ R3 be the lineal transformation defined by LAX) : Ax, Where Then the dimension oi N (LA) is at I b. 2 @ d 4 e None of these 6‘ On the other hand, the dimension of Ram) is e 1 GE 0 3 di 4 e‘ None of these M 7‘, If L : R5 -+ 1R3 is ANY linear transformation such that the dimension of RUE) is three, then the dimension of N(L) is e 1 Q3 0. 3 d 4 e. None of these 8. if L : R4 ——+ R4 is ANY linear transformation such that N(L) n {0}, then the dimension of R(L) is a. 1 b. 2 c. 3 @ e. None of these OOH CON! 0 2 O Osfi-M QWH ...
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