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Applied Finite Mathematics HW Solutions 45

Applied Finite Mathematics HW Solutions 45 -...

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Unformatted text preview: /'—‘-. .r-"a._ EXERCISES 3.4 43 17. We present a sequence of elementary row operations that lead to a row echelon form for the augmented matrix of the given system. You may, however, use a different sequence of operations, resulting in a different rowr echelon form. The solution of the system, however, must be the same. 1 1 —2 4 1 l ~—2 1 3 1 6 R2—1—R14-R2 we 0 2 3 3 -—1 2 7 Rafi—3R1+R3 0 —4 8 1 1 #2 —> 0 2 3 0014 2 —5) R3—12R2+R3 l1 1 1 *2 4 2 sadism —. 0 1 3/2 1 ~1 Rg—DR3/14 - o o 1 —1/14 We now convert this augmented matrix to an equivalent system of equations, :c+y—2z=4, y+§z=1 2 I z=_i. 14 When we substitute 2 = *1/14 into the second equation, we obtain + ——— => —1+3—El 3" 2 14" 3" 28‘28' When we substitute 3; = 31/28 and z = -—1/14 into the first equation, we get 31 1 31 1 11 m+-——2(—-—)—4 => m-4~§-§—?_T. 18. We present a sequence of elementary row operations that lead to a row echelon form for the augmented matrix of the given system. You may, however, use a different sequence of _ operations, resulting in a different row echelon form. The solution of the system, however, must be the same. ' - 4 1 —2 4 Rl—r—B,§+R, 1 2 —4 —3 2 3 1 s -—-—-—) 23 1 6 Rg—r—2R1+Rz 3 #1 2 7 3 —1 2 7 Rafi—3R14-Rs 1 2 —4 —3 . 1 2 —4 —3 —¥ 0 -1 9 12 R2 —> —R2 —-* 0 1 -9 ~12 0 L7 14 16 O —7 14 16 R3 —> 7R2 + R3 1 2 —4 —3 1 2 —4 #3 —1 0 1 —9 ~12 —) O 1 —9 —12 - 0 0 —49 —68 3,; —> 413/49 0 D 1 68/49 We now convert this augmented matrix to an equivalent system of equations, w+2y-—4z=—3, y—Qz=#12, z—@ _49. When we substitute 2 = 68/49 into the second equation, we obtain 4. _:_| n. __ I. ___ _____ Lu”) :_ -......_A'.._.... "at. nnMn—Jn‘l. In“. I." it... 'l'lninmilunI‘II-anflnka nanlrdnm 11""th ramxflnnfim I-fl nnrf hr in HI“ 3!: £1!"le mhlhi'lfl‘l. ...
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