Eigenvector - Linear Algebra - Quiz Solution, Exercises of Linear Algebra

Download Eigenvector - Linear Algebra - Quiz Solution and more Exercises Linear Algebra in PDF only on Docsity!

Math 2054 Quiz 07 page 1 November 14, 2008 oe L242 samme | 9 11 atte win [) 2 9 -5 3 1A. Is v an eigenvector of A? Explain. If it is, give the eigenvalue. rr 2 s se z ite ie . Ava") =e] the 7, so yee G6 tm ejtnoedorg A became CAO Ord Hose erat NR of AAZ2hv, 1B. Is w an eigenvector of A? Explain. If it is, give the cigenvalue. fir] oe [oh ANE] E09 f, [iToae m t 1C. Fact: One eigenvalue for A is \ = 4. Find a, basis for the corresponding eigenspace. ele Ey "he z ral & a Lawes as as null pace -5 nino? 4] ‘ee oe Ip. 2a. Find the characteristic polynomial of C. : Chae pay (c) 2 de{(-)I.) = a a = (B-N7-»)-24= 2-04 N24 2 2b. Find any real eigenvalues of C' or explain why there are none. =/A ~/0r-3 : j= 0 t/0- HY _ tox faa _ texte? , 227 [Sah 2 2] 2 3. Suppose B and D are 4 by 4 square matrices and Det(B) is 4 and Det(BD) is 8. Find each of the following. Write “Can't Do” if it is not possible to find the answer with the information given. a. Det(D). 2. | Since nea ne (0) to), 8)= —_b, Det(DB). [el] ) OO (ches OB EBD rgoent) d. Det(B-!). c. Det(BT). 4 #8 oxide, hun I= dite (1) = die(B8*) = At (2) to) ~4. | f. Det(B3) ef = AM dtlo}daloe 599 h. Det(B + D) Pee 4 (38 5 dbad fom B by oe Dense): Pets aH nts KH ites cuba lio oll 4) Hats lit g. Det(B + B) GH a tebor 3) = Let (28) = 2". dita) = 24.45 a