Solutions - Linear Algebra - Solved Exam, Exams of Linear Algebra

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NAME: Ss LuTren§ Math 205 - Exam 1 - February 3, 2006 1. (8 pts.) Describe all solutions of Ax = 0 in parametric vector form, where the matrix A is 1-4 -2 0 2-68 #1 3}. 0 1-193 How can these solutions be described geometrically? a ws reduce ty mcduced ale at Ale ausey nese tech trccbrix [A 2 | Pale (PES Te) ec lng ln een. Mee erage { oS Fe! 9=o pr4e2 oo 7} 2-48 tl 30 ~ ° ° 3 30 |” 6 ()-1 30 | Cn iteae oa 0° hse | aes 8 oso | Ue Tet) Lo Gceetal ~ Oo See oe |i 'g 6 ‘ a pl Ror aienee: oe ape EERO Vion} The solubrrsen all pts Ss x, + eee) ae ity oe PG OS eee ja hee Se te kee ie origin andl Gt -14)} Kat Kycia Li lox st - Kay Free. Z 2. (8 pts. ench) Consider the trafisformation T : R4— R&, given by T(x) = Ax, where A is row equivalent to aan tees {a) Does T map R* onto R4? Explain. {b) Is T one-to-one? Explain. ss 1 = 3 ay Sine mite it Ax= Mes a golucho fir off PotatR. Sie Aare preal iateacl mest by pele PEACE ha ts chin ha, AREG alwags bev a solution, %* T is onto, DW tg Ve Bee ee ees Selle tho ex et most 3 prvel we hove Smee Ay che St Ce faves aud 3 rw, (Ale ore exoctly 3 pivots, achutl,}, So tn Axes , & fee vervell, s- Tis Moet. Wks