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

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Math 205A Quiz 5, page 1 October 26,2007 = NAME (Suggested 120280 Dn 38 ged DI Oe, jotion lLet b=} 2 10)/,U=]03 1 0/,andAs 4 91 8 |. Suppose A= LU. 01 -5 31 0 0 -10 ¢ 3 -19 1A. What is the value of t? (What expression did you evaluate to find it?) a a eT 7 secrgeeely mee 1B. Use the method of LU decomposition as discussed in class to solve Ax = b, where b = 2 | : —3T Show all your steps. Write the solution as p+ -v, where p is a particular solution of Ax = b and v, gives the solution(s) of the corresponding homogeneous equation. 2304) Ax=6 => w fa[-) ot F= Us 5 Salve jest] fe a luz=6 9 See ts LqGaba oy "i dete etn, = > 3 x32 ee, % 4 z =| = - a || | :[2 | Fag t =-6> * (4 tn tx) $3 6) = * 2 ooo p) =f (4-4(-2-4s3)-4) : (in Baal e fy, +72? S422 242(6) =4(6 a: 9) a : = = 32498 = % Ks Benes iu Sy, by, 12 = SPD WI RF BT) a2 0 4 3 1C. The augmented matrix [Alb] is row equivalent to | 0 1 1/3 0|—2 |. Use this fo again v O20 Oe lel the solution of Ax = b as p+). How does this solution compare with the one from 1B (is the particular solution the same?) - L af Beat (oe he io, (ete Mee, X= |e [om | PY puasee is Or 1 x; ° c oro [| +0% 23 4 1D. What one elementary row operation changes A into | 4 9 8 |? (Deseribe it: “Row 3 is f O * 1 teplaced by ...”) ( £ +5 rasfelwed) mn A, t6-6 arta = -@ +&-8 =-G6tls LF. What elementary matrix E corresponds to, or, carries out this operation, if you compute BA? Po fo Ty Wihed Yoo Liiwt 4 ilo eA, Had &, replace is Phicd vet by fe SR, 5 Since [y= ae oe Hrs yids E= 21] d 50] 1E. What is the value of + after this operation?