This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
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. LA1123;o—==.> —ﬁ —?—ﬂTS_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 ...
View
Full
Document
This note was uploaded on 10/08/2010 for the course NE 112 taught by Professor Vanelli during the Spring '10 term at Waterloo.
 Spring '10
 Vanelli

Click to edit the document details