Solution Manual for Finite Mathematics And Its Applications 17th Edition by Larry J. Goldstein

Chapter 2 g




Instructor’sgSolutiongManual
Exercisesg2.1 ⎨
⎩g–5xg+g4yg=1
⎧⎪ 1gxg–g3yg=g2 [2]+5[1]g g ⎧gxg+g2yg=g3
1. ⎨g2 ⎯g⎯⎯g ⎯⎯g →g⎨ ⎩
⎪g⎩g5x+g4yg=g1 14y
⎧gxg–g6yg=g4
2[1]
=16
⎯g⎯⎯g →g⎨
⎩g5xg+g4yg=1
4. –g g(first)g –g gxg+3yg=g–2

⎧gxg+g4yg=g6 (–1)[2] ⎧gxg+g4yg=g6 +(second)g xg+g2yg=1g
2. ⎨g ⎯g⎯⎯g ⎯g→g⎨ 5yg=g–1
⎩ –gyg=g2 ⎩ yg=g–2
⎧g⎪gxg–g6yg=g4 [2]+ ( )–21 [1]
g g g ⎧gxg–g6yg=g4
3. 5(first)g 5x+10yg=15g+g(second) – ⎨g1gx+g2yg=1g⎯g⎯⎯g ⎯⎯g ⎯g→g⎨g⎩ 5yg=g–1
5x+g4yg=1
⎩g⎪g2

14yg=16 5. –4(first)g –4xg+8y–g4zg=g0g+g(third)g4xg+gy
⎧ xg+2yg=g3 +3zg=g5

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,ISM:gFinitegMath Chapterg2:gMatrices


19. Useg[1]gtog(–2)[2]gtogchangegtheg2
togag0.
9yg–gzg=g5
⎧gxg–g2y+gzg=g0 20. Useg[3]g+g(–4)[1]gtogchangegtheg4
⎪ togag0.
⎨ yg–g2zg=g4
21. Interchangegrowsg1gandg2gorgrows
⎪g 1gandg3gtogmakegthegfirstgentrygingro
⎩g4xg+gy+g3zg=g5
wg1gnonzero.
⎧gxg–g2y+gzg=g0
⎪
[3]+(–4)[1] ⎛g1⎞
⎯g⎯⎯g ⎯⎯g ⎯g→g⎨ yg–g2zg=g4 22. Useg⎜g– ⎟g[2]gtogchangegtheg–
3gtogag1.
⎪g
⎩ 9y–gzg=g5 ⎝g3⎠

6. 3(second)g 3y+g9zg=g3 23. Useg[1]g+g(–3)[3]gtogchangegtheg3
+(third)g –3y+g7zg=g2 togag0.

24. Interchangegrowsg2gandg3gtogmake
16zg=g5 gthegsecondgentrygingrowg2gnonzer

⎧gxg+6yg–g4zg=1 ⎧gxg+g6yg–g4zg=1 o.
⎪ [3]+3[2] ⎪
⎡g3 96⎤g1
⎨ yg+3zg=1g⎯g⎯⎯g ⎯⎯g →g⎨ yg+3zg=1
25. ⎢g⎣g2 86⎥g⎦g⎯g⎯⎯
⎪g ⎪g
⎩g g –3y+g7zg=g2 ⎩ 16zg=g5 3[1]→g⎡g⎢g⎣g21 38 26⎤g⎥g⎦
⎡g1g–g1
7. ⎢g⎣g0 21 43⎤g⎦g⎥g⎯g⎯⎯ [2]+(–2)[1] ⎡g1g g 3 2⎤
[1]+12⎯⎯g [2]→g⎣g⎡g⎢ 01 ⎯g⎯⎯g ⎯⎯g ⎯g→g⎢g⎣g0g2g 2⎥g⎦
0154⎥⎤g⎦ 7
1
⎡ 1 3 2⎤
2[2]g g g g
–2
8 ⎯g⎯⎯g →g⎢g⎣g0g 1g 1⎥g⎦
⎡g1 09⎤
⎢ ⎥ [1] +(–3)[2] ⎡g1g g 0g g –1⎤
8. 0 13 ⎯g⎯⎯g ⎯⎯g ⎯g→
⎢g⎥
⎢g⎣g0 45⎦g⎥ ⎢g⎣g0 1
⎡g1g g 0 9⎤
[3]+(–4)[2] ⎢ 1 ⎥ 1⎥g⎦g xg=g–
⎯g⎯⎯g ⎯⎯g ⎯g→g0g 0 3
7g– ⎥
⎢ 1,gyg=g1
2g16g
⎢g⎣g0 –7⎥
⎦
17. Useg[2]g+g2[1]gtogchangegtheg–2gto
ag0.


18. .gUseg g[2]gtogchangegtheg2gtogag1.




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,ISM:gFinitegMath Chapterg2:gMatrices




26. ⎢ ⎥
⎡g13 261⎤g⎦g⎯g⎯⎯ 3[1]→g⎡g⎢g–21 –4663⎤g⎥g⎦g 28.g⎢g⎢ ⎡g–4 –71
03–314⎥g⎤g⎥
⎣g–2 –4⎣
[2] +2[1] ⎡g1g 6 3⎤ ⎢g⎣g6g g 14 750⎥g⎦

⎯g⎯⎯g ⎯⎯g →g⎢g⎣g08 12⎥g⎦ ⎡g1 2 08⎤

1[2] ⎡g1g g 6 3⎤ ⎯g⎯⎯g 2[1]→g⎢g–4–7 3–31⎥
8⎢g⎥
0
⎯g⎯⎯g →g⎢g⎣g0g 132g⎥g⎦ ⎢g⎣g6g g 14 3 750⎥g⎦
1 0–6
[1]+(–6)[2] ⎡g ⎤ ⎡g1g 28⎤g g 7

⎯g⎯⎯g ⎯⎯g ⎯ →g⎢g⎣g0 132⎥g⎦g g ⎯g⎯⎯g [2]+ 4[1]⎯⎯

→g⎢g⎢g0 11⎥g⎥

xg=g–6,gyg= ⎢g⎣g6g1450⎥g⎦
⎡g1g 2g0
8⎤
[3]+(–6)[1] ⎢g⎥
⎡g1 –3 41⎤ ⎯g⎯⎯g ⎯⎯g ⎯g→g⎢g0g 1
31⎥

⎢g ⎥
27.g g 4g –10 104 ⎢g⎣g0 2 72⎥g⎦
⎢g⎥
⎢g⎣g–3 9 −5–6⎥g⎦ [1]+(–2)[2]g g ⎢g⎡g1g 0 –66⎤g⎥

⎡g1 –3 4 1⎤ ⎯g⎯⎯ ⎯⎯ ⎯g→g⎢g0 1 31⎥
[2]+(–4)[1] ⎢g ⎥ ⎢g⎣g0 2 72⎥g⎦
⎯g⎯⎯g ⎯⎯g ⎯g→g 0 2 –6 0
⎢g⎥
⎢g⎣g–3 9 –5 –6⎥g⎦ [3]+(–2)[2]g g ⎢g⎡g1g 0 –66⎤g⎥

⎡g1 –3 4 1⎤ ⎯g⎯⎯g ⎯⎯ ⎯g→g⎢g0 1 31⎥
[3]+3[1] ⎢⎥ ⎢g⎣g0 0 10⎥g⎦
⎯g⎯⎯g ⎯→g 0 2 –6 0
⎢g⎥
⎢g⎣g0 0 7 –3⎥g⎦ [1]+6[3] ⎢g⎡g1g 0 0 6⎤g⎥

⎡g1g g –3 4 1⎤ ⎯g⎯⎯g ⎯→g ⎢g0 1 3 1⎥

⎯g⎯⎯g 12[2]→g⎢g0g 1 –3 0⎥ ⎢g⎣g0 0 1 0⎥g⎦




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, ISM:gFinitegMath Chapterg2:gMatrices




⎢ ⎥
⎢g⎣g0 0 7g –3⎥g⎦ [2]+(–3)[3]g g ⎢g⎡g1g 0 0 6⎤g⎥

⎡g1g g 0 –5 1⎤ ⎯g⎯⎯g ⎯⎯g ⎯g→g⎢g0g 1g g 0 1⎥
[1]+3[2] ⎢ ⎥ ⎢g⎣g0g 0 1g 0⎥g⎦
⎯g⎯⎯g ⎯→g 0 1g g –3 0
⎢g ⎥g
⎢g⎣g0g0 7g –3 ⎥g⎦ xg=g6,gyg=g1,gzg=g0


⎯g⎯⎯g 1[3]→g⎡g⎢g⎢g01g 01 –3–5 01⎤g⎥g⎥ 29. ⎣g⎢g⎡g23g –24–
41⎥g⎦g⎤g⎯g⎯⎯g 21[1]→g⎢g⎣g⎡g31–14–21⎥⎤g⎦
7



⎢g⎣g0g 0 1g g – ⎥g⎦ [2]+(–3)[1] ⎡g1g g –1g g –2⎤
⎯g⎯⎯g ⎯⎯g ⎯g→g⎢
⎡g1g g 0 0g g –g78⎤ ⎣g0 7 7⎥g⎦

[1] +5[3] ⎢g⎥ 1[2] ⎡g1g g –1g g –2⎤
3
⎯g⎯⎯g ⎯→g ⎢g⎢g⎣g00g01g 7g –31 3
0⎥g⎥g⎦g ⎯g⎯⎯g 7→g⎢g⎣g0
1g1⎥g⎦
–g7


[2] +3[3]g g ⎡g⎢g1g 0g g 0g –g879g⎤g⎥ ⎯g⎯⎯g [1]+1[2]⎯→g ⎣g⎢g⎡g01 01
–11⎤g⎥⎦
3
7

⎯g⎯⎯g ⎯⎯g →g⎢g0g 1g g 0 –g7g⎥ xg=g–1,gyg=g1
⎢g⎣g0g 0 1g g –g ⎥g⎦

xg=g–g g,gyg=g–g g,gzg=g–g

1 2
30. ⎢g⎣g⎡g–12g 23 – 21[1]
→g⎡g⎢g⎣g–1 2 –2g ⎦g⎤g⎥g 32.g⎢g⎢ ⎡g11g–12 –12
24⎥g⎦g⎤g⎯g⎯⎯
–411⎥g⎥g⎤

⎡g ⎤
[2]+1[1]g g 1 2 ⎢g⎣g2 5 939⎥g⎦




39