{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

exam3 - (l(~~ S 1 00 L&'1A)v\N 1\~ ~ ~ dCA~rc t.e...

Info icon This preview shows pages 1–4. Sign up to view the full content.

View Full Document Right Arrow Icon
).-z ~ = SOL UI) OJ\! Math 203-001 Spring 2011 Exam 3 Name: Last First (P robl em 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 - \
Image of page 1

Info icon This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
[ 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
Image of page 2
Image of page 3

Info icon This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Image of page 4
This is the end of the preview. Sign up to access the rest of the document.

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...
View Full Document

{[ snackBarMessage ]}

What students are saying

  • Left Quote Icon

    As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

    Student Picture

    Kiran Temple University Fox School of Business ‘17, Course Hero Intern

  • Left Quote Icon

    I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern