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

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Math 2054 Quiz 02, page 1 September 21,2007 NAME Suggectedl solutions ‘ dee foi 6 I : me : 1. Find | 0 1-3 2 3) ese! tO HA 25 -7 10 2 24540 ce oO : #044 GtgS tO+20 2. Let A be the 3 x 4 matrix from problem 1. Express all solutions of fell = bin the form p+vp, where p is a particular solution of Ax = b and vy, represents all solutions to the corresponding ce" il wor uN 70 homogeneous equation Ax = 0. Here, b= | 20]. 120 10 4 0/10 Hint. | 0 1 —3 2) 20 | is row equivalent to the augmented matrix you would set up to begin 0-0-6. 0:] 20 fs solving this problem. A eee h ne . amiss [ey a = Kab fe 32 Ila | [Po te fav - ~ eGgvitelent madyix &h us He soblhins f Y 12 $ -3 40 i na a x) =/o -Yx. 3 le “4 0 X, #20 + 3% -2Xy _ |20 : 2 . a % ob free. a oO 3 I ee 3 %y ® fee 0 o : a ———————— P Vn Nore : it may hulp to ( X,> 10 -Hxy + Oxy wre 7 X22 edn, ~2%y fo -Ony Se ai) Ky 2 O+ Oxy t 14 3. Let A and b be asin problem 2. Let aj, ag, ag and ay be the columns of A. Use your answer to (2) to express b as a linear combination of aj, ag, ag and a, in 3 different ways, the first of which should be by setting all free variables to 0. Make clear your choices of values for the free variables. (See on-board example). LCi: wee Pol hb we Xp = XysO. This gues x,2/0 and x,2 20, Ger LE x (0% + 20a, (07, 108, + 208, + Ob, tO4, a LC2: te 102 8 ie 2, Phone ae 0D -1Many powible Anions « Connon, LC 3: Seen an stidenk' Guitrec wire flue Cramples - © Choose %=1 ac Get Ga, + 23a, + &, @ Xpel an Xy = | Gk ba, + 2a, +&, 44%, 9 ae G& La, + 124, +28 +20, et. (Go x)= 0-822 ok Mp0 qQ3}x{20-2) ate 22 )