108B-hw's

# 108B-hw's - (due Oct 20 in class from the textbook Chapter...

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MATH 108 B ADVANCE LINEAR ALGEBRA WINTER 2011 HOMEWORK #1 (due Oct. 4 in class) from the textbook Chapter / Section / Problems : 3 / 2 / 2(f), 4(b), 5(d), 6(b) /// 3 / 3 / 3(c), 8 /// 3 / 4 / 2(b), 5 /// 4 / 2/ 10 EXTRA PROBLEMS : 1) Let V 1 ,V 2 ,...,V n be a ﬁnite collection of sub-spaces of the vector space E . Prove that the union of V 1 ,V 2 ,...,V n is a sub-space of E if and only if there exists j = 1 , 2 ,..,n such that V j contains all the V k ’s, k = 1 , 2 ,..,n . 2) Given the vectors ~v 1 = (1 , 1 , 0) , ~v 2 = (0 , 1 , 0) , ~v 3 = (0 , 0 , 2), describe geomet- rically the following sets B 1 = { ( x,y,z ) R 3 : ( x,y,z ) = 3 X j =1 α j ~v j , α j 0 } , B 2 = { ( x,y,y ) R 3 : ( x,y,z ) = 3 X j =1 α j ~v j , 0 α j , 3 X j =1 α j = 1 } , B 3 = { ( x,y,z ) R 3 : ( x,y,z ) = 3 X j =1 α j ~v j , 0 α j , 3 X j =1 α j 1 } , B 4 = { ( x,y,z ) R 3 : ( x,y,z ) = 3 X j =1 α j ~v j , 3 X j =1 α j = 1 } . HOMEWORK #2 (due Oct. 13 in class) from the textbook Chapter / Section / Problems : 4 / 3 / 4, 10, 11, 12, 15, 19, 20, 21. HOMEWORK #3
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Unformatted text preview: (due Oct. 20 in class) from the textbook Chapter / Section / Problems : 5 / 1 / 2 (b), 3 (b), 3 (d), 4 (a), 4 (c), 8, 14 * , 17 * HOMEWORK #4 (due Nov. 1 in class) from the textbook Chapter / Section / Problems : 5 / 2 / 2 (d), 2 (e), 7, 8, 11/// 5 / 4 / 3, 17 ** HOMEWORK #5 (due Nov. 8 in class) from the textbook Chapter / Section / Problems : 6 / 1 / 8(a), 8(b), 11, 21(a), 23 (a), 23(c), 24(b), 24(d), 26 /// 5 / 4 / 19. HOMEWORK #6 (due Nov. 15 in class) from the textbook Chapter / Section / Problems : 6 / 2 / 2(a), 2(b), 11, 12, 13, 19 //// 6 / 3 / 2(a), 6, 7, 8, 12. Extra credit problems (due Nov. 21, before noon in my mailbox) Typeset by A M S-T E X 1...
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