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**Unformatted text preview: **Math 221, Winter 2016, Section 202 Page 1 of 3 Quiz V
February 9, 2017 No bOOks. No notes. No calculators. No electronic devices of any kind. Name Student Number Problem 1. (4 points)
(a) Given: the n x n—matrix A cannot be row-reduced to In. Are the columns of A linearly independent or linearly dependent? Or is there not enough
information to tell? A amok ‘02. MW; be in Ynzpms Ha. AlﬂoV‘H‘M
Ms, 9, A 8 Mr .Mwhm, ”0% m comm, W41, a;
W- {\Wﬂgwm W m we? 01 A mimic“ 9““
l“ WMMMW MM»: RQEFUD :1“ mm A Mum a»
rm qwhlm to '1M \ {luv invethE A (b) Suppose A is an n x n-matrix with the property that As? = 5 is consistent, for
every b E R”. Does An? = 6 have a non-trivial solution or not? Or is there not
enough information to tell? \? IAN/€91; IX cwubwl ‘N x“ C, 443% RE$CPA mag prltvxeu-ha W- ngx A 3) $1M) REEFLM has « Fuel \V‘ 1W3 Coll/UM“ , 30 cHw-k m W Quuamm “A ”>93- $° Ai=3 km on MW?¢luh\Tv\_ Math 221, Quiz V Page 2 of 3 ---—| Problem 2. (6 points)
(a) Assuming A, B and C are n x n—matrices, with B invertible, solve the equation AB=BC fOIC- WW7 ‘13 WNW: Wimp—MC :1“
SC" VHS! (b) Assuming that A, B and S are n x n—matrices, with S invertible, solve A=S'BS'1
for B. Mllﬁva h] S" W ,Qn/P‘ ““4 S m n3“ ‘,
WAS: 37§T5§73 (c) Assuming that A and B are invertible n x n-matrices, write (AB)‘1 in terms of A‘1 and 3—1. _‘
(A 3) mm" —. I“ out»; (A93 . depB ‘13 (3“A" ow “9.2+ “in 5(1va (16‘! (3qu v A" As (ARV = V033
WM
In 90 Q63)" : 75" A" . Math 221, Quiz V Page 3 of 3 Problem 3. (10 points)
Consider the three matrices 3 4
2 0 —1 2 3
A4215), B—(j g) 0-(3 4,).
Compute the following expressions (if they are deﬁned).
2 0 ,‘ '2 ‘I 2.3 4- up“ mom 1“}40‘04 («57.)
(Q AB== (,1 .~§) ’1 0 ' (Lﬂ3+ua)+<vo ’rw*P0+91 __ (yo-H 810—1 : (7- LB
' (’Q‘l-Y '8 Ivo-HO _'3 2’ (mg/1: ‘4 ‘* (7. o 4 _ z-w-u 3.0m WM
'L D ~1 1 s " -L1+ma) ao~o: cowvwr ~\.‘1 » 101) +0 ‘l-| (dyq) tl-T 9-9; ow :yzo ,‘L H I?
= —‘|'0 M 240 : “f 0 2
44* on. we ,3 1 ll '1) —§ '7. O m5!L 44M .
'l 'L
3 u-ﬂr‘ﬂ-S) 31-3)”;
_ I _ _ / , , - (’3). -
((1)30 1 : (.1 o if, 3" '5 = I '3 -1(Y)t0(3) 1 07'
4 L 1(§)-33 ’3 2 ° 4”)va «(Inn-L
4? 4L ‘1 4 3 “Z? 'l
I l (o co 6’0 - ’0 Q
5-; 3*% -( ?
<e)<BC>-1 : ( y ) "
W ...

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