exam1 - pan s wIth coefficient 3 11" o.il directions...

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I S OlUl (J / j Math 203-001 Spring 2011 Exam 1 Name: Last First (Problem 1) (25 points) Find the general solution of the linear system (please write the solution in the vector form) or explain why the system is inconsistent . 2- { Xl -X2 +2X4 53 X2 -3X3 2Xl -X2 -3X3 +4X4 = 13 \~ l I I - \ rv 0 \ o =~ ~ \ ~ 1);\ ~ L~ - ~ ~~ ~ --:x 3 == t\ :c ~ -=- -l 2.. ~ 0 [JJ -~ ~ 0 -3 0 ~] Y' \ -:::. g + '3> t \ - L -t 2. (J 0 0 C) :x.:) .:x ~ J:. :=: 3 + 3-t \ )C Y.l 2- \ / ~ - L- ee. ¥\( -:J(U XI ~ 3 ;y:.z 3 -t2- 0 3 1- t) -\- 0 I :£3 - 0 - \ 3~ 0 0
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(Problem 2) (25 points) Determine whether the set of vectors al , a2, a3 is linearly independent or linearly dependent. 1 0 3 0 1 -1 2 1 5 al = 1 , a2 = 0 ,a3 = 3 0 -1 1 - 1 1 - ~ 0 3 \ 0 3 tD O L \ ".., ~ 0 I -\ 0 I -I i) () tn-I 2- I S- O I -I 0 0 0 rv tl r-IJ ~ I 0 3 0 0 0 0 C) 0 0 -\ \ o -I I -\ 0 0 0 +1 -I I -!j 0 - / 0 0 0
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(Problem 3) (25 points) (a) Find the ." , " TA : ]R2 ---> ]R2 that first ex d "matllx A of the Imear transformation reflects across the x2~ax is . '
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Unformatted text preview: pan s wIth coefficient 3 11\" o.il directions, and then (b) Find the imag d I e un er t le transformation T f th -[2] A 0 e vector x = (b) Find the vector y _ [ YI] 1 " - 1 " _ -Y2 W lose Image under the transformation T A is the vector b = 6 9 " [~ J A ::t~ ~ J A -r -I 0 J [~ 0 1 - [-:) 0 J - L 0 \ · 0 3J -0 3 [ 1 2 0 1 (Problem 4) (25 points) (a) Find the inverse matrix to the matrix A = 1 1 0 . 051 (b) Use the result of part (a) to solve the following systems of equations: [ \ Z. 0 \ 0 0 \-1 [\ 2. 0 \ 0 0] [ A I I 1 =-, I a 0 lOW-N 0 ~ \ 0 -\ I 0 \ t S-3J 0:; 1 001 0)"1 COl ~ [ \ 2.. 0 \ \ 0 O]J ~\ 0 C) r---' 0 -\ 0 -/ \ 0 +.2. ~ 0 - \ 0 o 0 \ -S" 5 \ C) 0 \ - \ 2 0] -\ I 0 1((-0 -s-S-I ( ~ (-I 2. 0 / 1 -\ 0 -j :Y \ \ \\ \ l~ If l .:L \ 1 -\ r I 1 r -l L 0 J l \ J f -\ j ~~ = A t g j :: l~ -~ ~ . g :: t~ _ \ 2 0 0 (-I). D -t 2 ,2. to, \ ~ 2,) r l T~ 0 'L 1,0.,. .(-1\2 ,() . I --2. I - \ -~L ---S ~rS1 ~ ~ x.) -) S \ (-)) .0 + S-' 2 -1\ \ \ \ \ r...
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exam1 - pan s wIth coefficient 3 11" o.il directions...

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