Practice Midterm Questions_2009_and_solutions

Practice Midterm Questions_2009_and_solutions - Sam le...

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Unformatted text preview: Sam le Midterm uestions for NE] 12 Linear Al ebra with Numerical Methods Fall 2009 Question 1: Answer whether each statement is True (choose A) or 1: also (choose B) (a) For every invertible n by n matrix A. there exists a nonzero n by n matrix B such that 1: ABisthezeromatrix.® 53:6 =5 5:,“Ag : A‘l q =_a :3 13:0 (b) lftwo invertible Infiltrices A and B commute. then A'1 and [3?1 must commute as well. 1’ 52139 :9 marl ; Lian)" '1’ .8“A"I : A" (3" (c) lfA is a 3 by 3 matrix such that {A + l3): = 0. then A must be invertible. L _ '7’ AH. LA1-123;o—==.> —fi —?—fl--TS_I 5 0 3 => M—fl “'13 J =13 an =-A~z§ (d) The matrix 0 0 0 is in row echelon form. r0 ,- L “4“” 1'4. ,c 0 — 2 5 in” 1 3 l l 3 l /’ (e)Thematrix 0 4 ~55 is similarto 0 2 4 l 0 2 4 l 5 —3 l 3 \ Question 2: {TJaY‘3 : :"9'1 ‘ t 5" -} The following system of equations has _ 7 solution(s). x + y =2 6x + 6)! = 12 as) 1 4c; :- 1-— @infinite (B) no (C)tw0 (D) unique Question 3: 5‘ 'L—» j s f 7 Find all .s‘ and I so that B” : 0 if B 2 0 0 S I 2» (A)There are no such .s’ and r :7 (B)r:0ands ER (C).s'= Candi: O (D).s' = 0 or! : 0 @=OanthR (FM: 1 andI:—l Question 4: 1 1 2 IfA = l 0 l . which one ot‘the following statements is true for A“? 2 1 4 @The third row is [-l -I ll (B)The second column is [0 2 (C) The first row is [2 0 -I] (D) It does not exist (E) Each of B. C. D. and E are true -1 1'" (F) The second row is [1 2 —1| ‘0 ‘ P l 0 a o a l O V l (L l a v I I I o a o l ‘9 l L t o a l Solutions: 1 ) 21) False b) Ter c) True d) False e] Ter 2)A ...
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This note was uploaded on 10/08/2010 for the course NE 112 taught by Professor Vanelli during the Spring '10 term at Waterloo.

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Practice Midterm Questions_2009_and_solutions - Sam le...

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