Exam3 - (l(~~ S 1 00 L&'1A)v\N 1\~ ~ ~ dCA~rc t.e U"k ~ ~c o·v-1 G ~~ 7 L" I(2(Problem 3(25 po;nl G;ven veclorn U ~ ~ l u ~!l l y ~[~

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).-z ~ = SOL UI) OJ\! Math 203-001 Spring 2011 Exam 3 Name: Last First (Problem 1) (25 points) For the matrix A = [ ~ ~ ] do the following: (1) Find all eigenvalues; (2) For each eigenvalue, find the basis of the eigenspace; (3) If it turns out that A is diagonalizable, find the corresponding diagonal matrix and the change of coordinates matrix. X I -=-2 ) A - ~ 2 , tY CJ J~~~ \ c{ c c \0 I,.l;. h..C\.~ 't 'y - \
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[ 1 1 2] (Problem 2) (25 points) Given matrix A = 0 0 0 and vectors -1 -1 -2 ,,~ [ ~2]' v ~ [ ~~ ] , w ~ [ i 7 ], detennine (with explanation) which of the vectors 'ii, V, ill are eigenvectors of matrix A. "L o 0 l -l -2 -2- ~ \ ~ - l- I - L-1. 6 o () 00 l Z tc~
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Unformatted text preview: (l(~~ S 1 00 L \ &-'1A )v) '\N 1 -/ \~ ~ ~ dCA~rc-\ t..e ) U "k ~ ~c :::. . o·v -1 G ~~ 7 L-(,' (" ( I) (2) (Problem 3) (25 po;nl,) G;ven veclorn U, ~ . [ ~ l' u, ~ [ !l l' y ~ [~ l' do the following: 6 (1) Check that vectors Ul and U2 are orthogonal; (2) Find the orthogonal projection y of vector y onto the subspace W = Span{ul,u2}; (3) Calculate the distance from y to W . '\ -+-) ,2 2 .( -I) -::: () V 6 ; 1A. I r - I 2-I '1A( ·1A 1 2. l.--'" \\ 3 ~, +2( \) . ..Jrb*2·L --:1 -142.1. \1 2 1.. i ~ bl = l f - L \ ---v ---v "-<S .).2-" L -14 \'l-,2 --o o o 2-3 \ - 2 0 \ o +cH 0 -t2-2. \ 2 o 2. 2... -- := () /\/\A---D o L I --I o c o...
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This note was uploaded on 12/20/2011 for the course MTH 203 taught by Professor Fall during the Spring '11 term at George Mason.

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Exam3 - (l(~~ S 1 00 L&'1A)v\N 1\~ ~ ~ dCA~rc t.e U"k ~ ~c o·v-1 G ~~ 7 L" I(2(Problem 3(25 po;nl G;ven veclorn U ~ ~ l u ~!l l y ~[~

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