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Applied Finite Mathematics HW Solutions 41

# Applied Finite Mathematics HW Solutions 41 -...

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Unformatted text preview: (—1" .-’H“\ EXERCISES 3.4 - 39 8.‘ 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. 1 —1 4 7 1 —1 4 7 - 1 3 —.6 —13 R2-+-R1+R2 —> 0 4 —10 —20 Rag-+HR3+R2 2 1 —4 —10 R3—>—2R1+R3 (0 3 —12 44) 1 ~1 4 7 1 —1 4 7 4—, 0 1 2 4 _. o 1 2 4 0 3 ~12 —24 R3—+~3R2+R3 0 0 —13 —36 R3—1—R3/18 —14 2 1 SCI—I 7( 3) We now convert this augmented matrix to an equivalent system of equations, 1 0 :c—y+4z=’?, y+2z=4, 2:2. When we substitute 2 = 2 into the second equation, we obtain y+2(2) =4 => 4; =4-«4 =0_. When we substitute ‘9 = 0 and z = 2 into the ﬁrst equation, we get a:_0+4(2) =7 2» m=7_8=_1. 9. We present a sequence of elementary r011.r operations that lead to a r011.r echelon form for the augmented matrix of the given system. You may, however, use a diﬁ’erent sequence of operations, resulting in a different row echelon form. The solution of the system, however, must be the same. ' ' 1 1 —2 4 _ _(11 H2 4 2 3 1 —-6 Rae—211mm —» n1 5 —14 - 3 4 _1 _2 Rae—3R1+R3 0 1 5 —14)R3—>—R2+R3 1 1 _2 4 4—, n 1 5 _14 0 n 0 0 We nosr convert this augmented matrix to an equivalent system of equations, :c+y—2z=4, y+5Z:“14. When we solve the second of these for y in terms of 2, we obtain 3; = —-14 — 574. We non.r substitute this into the ﬁrst equation, \$+(—-14—5z)—-2z=4 2) m=4+14+72:18+72. Thus, there is an inﬁnity of solutions for the system :1: m 18 + 72, y m —14 — 52, z arbitrary. This main-1:4! I"... ha.“ Mung-I :“ "Mann,“ mm. mum-:44:- lnm 1.“. a... I T..:..m:+.. .d-‘l InukA'l... Dana—7AM muck". ..1..__.I....3:.... :_ .. "a m. :. a." :. ...:...I.. mum's“: ...
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