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psu261sp11tk2 - Ov of WD ‘HQN‘V Quclx wohlom...

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Unformatted text preview: Ov\ of; WD ‘HQN‘V: Quclx wohlom lQNw‘l’lN llPl‘S. mth 261 Test # 2 Name : This test is closed book. You may use your calculator ‘ 1. Use the shortcut formula to find the inverse of the 2 x 2 matrix. Kw WWW + l 2. Consider the matrix in II 82 01 (3.) Find the elementary matrices E1 and E2 such‘that EgElA = I. ‘ two ‘60 \ lo , Audi EBA“ °\1(:Dt \[Ol ' / (b) Write A‘1 as a product of two elementary matrices. , ~l GK 6‘ At t MWY‘S GiEl f: A A": [‘fleC'l , amt [mil-1‘ [W‘l] £251“ (c) Write A as a product of two elementary matrices. (1;ng : :1: means A t E: 9431:. affix Acuflf‘éfl Mel 3. Determine whether the collection 8 is a subspace of the R3. You must show work that justifies your answer. 331 8 is the collection of all vectors of the form x = [ 0 ] Where 173 = —a:1 . 373 CKng We qeflulfQMini o£ a SullKPAl/e‘ 0 ‘ ‘ ‘ X tOz—o :‘X (A\ “V1930 \jgg‘l’or _ [cg/1 13 m9 imce E | NM. A . gtMe x3: ~cu. : 'M J Cox GS, \lllljfi 4W2 CJMlCl‘NMS Sa‘llY‘ClQé/ S l8 m$ul03p4ce 6? {R3, 3 ~ 4. State a basis for the nullspace of the matrix. You'must show work that justifies your answer. K1“R\ ‘ I | 3 O Rf‘d’kz *3 O I —l 5 O ‘ % Kg'LWq O _4 Lf ‘10 0 l o 1 CF 0 k\'f:’% 0 ‘ “ I; U o O 0 O 0' (sum) X+0*1%*qw:o go ‘I '% +W=O ~Zs~¢t NC VUAUSPK(C Q/‘O‘M S'gf : S t : vkaM mg a (M633 2 3 4 0 5. For the matrix, ‘ A = I14 2 1 0532 state the following. Give justification for your results. dim<muzimm)~ A2 rank (A) , and nullity (A) - \-\1‘i [42“! ‘|~{2-I RH“ RyP. _ (242 ““3 i 4 1 I fl 0 5 0 6k L51 0 5-0 1 0 5 3 1 O 5 ? 1 O 030 T‘e chm/Acme rehiim cams we 4"" (oiMMV'i is A Cw“ (0,140;me of WC 09AM CDCUMVIS Cmti ‘Hf‘C girfi‘i‘ 3 Coiumm 4f? Qv/i \ tqsptmm/mfgh) :3. TM ”Amtfixm «Lou? Shes 3 2A rgws fLuj {(MKUXBZK ' 1kg Vtév’cf. Quwx ““0“ (0W3 I {We Varialgicij WAS nul'i‘iy (A):i\ 5 6. Use tho Gauss-Jordan Method on [A|I] to find the inverse of the following. Do by hand and show work. 1‘3 \00 Rvpl \oo‘ put» a \3 o l 0 fl 0 \ '3 o ‘ O '2. 1L} 00\ ngl 1 Q ( 04 I \ O U 1 'V‘ 0 R341“ 0 \ 3 o ‘ ‘0 g O O ‘ v1 ‘ \ (15393 ‘ o U ‘ g. L?) _\ ‘ 4 0 We \AVQYSQ Main 1 {g A j 6 ’2'; I? ‘2 \ 7. Let T : R2 —> R2 be the Linear transformation which rotates R2 counterclockwise around the origin by 60°. State the standard matrix for T. 6476) [T1 1'. C05 C00 “Siv‘ 600 “(70° 0:60” L J3 / 2 2- %- é qup _ L ~33 L? 5 ‘333 TH“ )‘ 1 I j l ’ ‘8' " 5% i 4 L13 +1 —o.°)64l0 1‘: 63%|} 8. Consider the linear transformation T : R3—>R3 givenby, 1:1 2 V 0 M) “i HWH (173 1 ‘ 1 State the standard matrix for the linear transformation. RurNW‘j) T67): Oxwoxl *2X] ‘3 M mix I) [\D Q ‘L *4)“. *1X} MUK‘E'F‘PCM‘Pi‘M fivm ‘ 9. For the matrix 5 1 A — [ 2 4 J . find all of its eigenvalues. Show every step of the process. _ \WMX) M [T A] :- Mammal « q1~qa~lovl : XL—MM?) v T @— GWV 3\ ”(\Q QlfiQV‘VAlmQS are, filté ’11:}. Find the corresponding eigenvectors of the eigenvalues. Show all your steps. 3‘36 ‘l l 0/] “l \ O 'X‘VVTO . [1“). b A O 00 <0) 73X " l M Wewvu‘ws we WNW €C€p¢m<[ D l 3n.“- 3 1 01:1“)] Ma“ Q,( ax, : o ’l . l O O o 0 30 ‘/:’1X “G‘C QifiEw VC CloYé QIG 3N0,“ by E? :5Pqn([vl2]) 9 ...
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