129a_ans1

# 129a_ans1 - Spring 2010 Answer of HW1 1.1#13 The solution...

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Spring 2010 Answer of HW1 1.1 #13 The solution is (5 , 3 , - 1). 1.1 #18 No. 1.1 #21 h can be any real number. 1.1 #25 The system is consistent if and only if k + 2 g + h = 0. 1.1 #30 - 1 2 R 2 R 2 , reverse: ( - 2) R 2 R 2 1.2 #1 rref: a, b ref: d none: c 1.2 #4 1 ± 3 5 7 3 5 ± 7 9 5 7 9 1 ± rref -→ 1 ± 0 - 1 0 0 1 ± 2 0 0 0 0 1 ± Pivot columns are 1st, 2nd, 4th columns. 1.2 #13 x 1 = 5 + 3 x 5 , x 2 = 1 + 4 x 5 , x 3 = free , x 4 = 4 - 9 x 5 , x 5 = free 1.2 #16 a. conistent and unique solution b. consitent and inﬁnite solutions 1.2 #30 x 1 + x 2 + x 3 = 1 2 x 1 + 2 x 2 + 2 x 3 = 3 1.3 #5 6 x 1 - 3 x 2 = 1 - x 1 + 4 x 2 = - 7 5 x 1 = - 5

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1.3 #10 x 1 4 1 8 + x 2 1 - 7 6 + x 3 3 - 2 - 5 = 9 2 15 1.3 #13 NO because the following linear system is inconsistent 1 - 4 2 3 0 3 5 - 7 - 2 8 - 4 - 3 rref -→ 1 0 26 3 0 0 1 5 3 0 0 0 0 1 1.3 #18 h = - 7 2 1.3 #25 a. NO, and there are 3 vectors in { a 1 , a 2 , a 3 } b. YES, inﬁnitely many c. a 1 = 1 a 1 + 0 a 2 + 0 a 3 1.4 #3
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129a_ans1 - Spring 2010 Answer of HW1 1.1#13 The solution...

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