Applied Finite Mathematics HW Solutions 62

Applied Finite Mathematics HW Solutions 62 - so EXERCISES...

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Unformatted text preview: so ' ' _ EXERCISES 3.5 23. We present-a sequence of elementary row operations that lead to the reduced row echelon form for the augmented .matrix of the given system. You might use a different sequence of operations. but since the reduced row echelon form is unique, you must-arrive at the same augmented matrix. 1 1 --1 1 --5 1 1 -1 1 *5 2 “3 1 “2 13 R2 -+ “2.31 -I- R2 _’ 0 --5 3 --4 23 R2 —¥ Re, 3 4 -1 1 "6 R3—+—-3R1+Rg U 1 2 ...2 9 R‘s—*Rz 1 1 0 2 “6 R4 -+ H31 *1" R4 0 0 1 1 --1 1 1 --1 1 “5 R1 -+ “R2 + R1 1 U “3 3 "14 _’ 0 1 2 —-2 9 _’ 0 1 2 ...2 9 0 —5 3 —4 23 R3 —! 5R2 + R3 0 0 13 -14_ 63 R3 -+ R4 0 0 1 1 r—l . 0 0 1 1 --1 R4 -+ 3.3 1 0 --3 3 ---14 R; '-+ 33.3 + R1 1 0 0 5 -17 _’ 0' 1 2 “2 9 R2 -+ “233 4- R2 _1. 0 1 0 —-4 11 0 0 1 1 -1 - 0 U 1 1 —1 0 0 13 H14 68 R4 -+ 1333 +34 0 0 0 “2'? 81 R4 —! —R4/27 l 0 0 5 —-17. R1 -+—-6R4+R1 1 0 0 0 1 _1. 0 1 0 --4 11 R2 -+ 434 + R2 0 1 U 0 -1 U 0 1 l -1 R3 -+ —-R4 + R3 0 0 1 U 2 0 0 0 1 “3 0 0 0 1 “3 The solution of the system is m = 1, y = —-1, z z 2, w = M3. 24. We present a sequence of elementary row operations that lead to the reduced row echelon ‘ form for the augmented matrix of the given system. You might use a difl'erent sequence of operations, but since the reduced row echelon form is unique, you must arrive at the same ' augmented matrix. 2 —1 4‘ 1 —13 121—1123 1 —3-1 0 -—«9 1 1 —-2 3 11 1 1 H2 3 11 R2—+—-Rl+R2 1 43 1 0 4-9 113.4131 _’ 2 —1 4 1 —-13 R34~2R1 +133 0 4 2' —1 1 0 4 2 —-1 1 1 43 1 0 —9 1 —3 1 0 -—9 _’ 0 4 —-3 3 20 _’ 0 4 —-3 3 20 122—1133 0 5 2 1 5 Re—+~R4+R3 o 1 0 2 4 Its—+132 0. 4 2 —-1 1 0 4 2 —1 1 1 —-3 1 o -9 Elemental 1 0 1 6 3 _’ 0 1 0. 2 4 _’ _, 0 1 o 2 4 0 4 _3 3 20 R3—+-4R2+R3 0 0 —3 -5 4 3342134+Ra 0 4 2 —1 1 R44~4R2+R4 0 0 2 —-9 ~15 1 0 1 6 3 R1H~R3+R1 10 0 29 29 _’ 0 1 0 2 4 ' _’ 0 1 0 2 4 001—-23—-26 001—23—46 0 0 2 —-9 —15 R4—+—-2R3+R«1 0 U 0 37 37 R4—4R4/37 Tm" “14.4.11 1...... 1...“... -MA..MA :n "mum. .1... mm. nn‘ODr-i'nI-ui 1....r I.“ nw I ham-sh“ n1! “want“. “rumba-Cm trunks.- fame-1:". in rm rf m- ;n H." :c «ax-nu nmh‘kiiar‘ ...
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