SOLUTION-MANUAL-FINITE-MATHEMATICS-AND-ITS-APPLICATION-9TH-EDITION-GOLDSTEIN

Instructor’s Solution Manual Exercises 2.1 ⎧⎪ 1 x – 3y = 2 1. ⎨ 2 ⎪ ⎩ 5x+ 4y = 1 2[1] ⎧ x – 6y = 4 ⎯ ⎯⎯ → ⎨ ⎩ 5x + 4y =1 ⎧ x + 4y = 6 (–1)[2] ⎧ x + 4y = 6 2. ⎨ ⎯ ⎯⎯ ⎯ → ⎨ ⎩ – y = 2 ⎩ y = –2 3. 5(first) 5x+10y =15 + (second) –5x+ 4y =1 14y =16 ⎧ x +2y = 3 ⎨ ⎩ –5x + 4y =1 [2]+5[1] ⎧ x + 2y = 3 ⎯ ⎯⎯ ⎯⎯ → ⎨ ⎩ 14y =16 4. – (first) – x +3y = –2 +(second) x + 2y =1 5y = –1 ⎧ ⎪ x – 6y = 4 [2]+( )–21 [1] ⎧ x – 6y = 4 ⎨ 1 x+ 2y =1 ⎯ ⎯⎯ ⎯⎯ ⎯ → ⎨ ⎩ 5y = –1 ⎩ ⎪ 2 5. –4(first) –4x +8y– 4z = 0 + (third) 4x + y +3z = 5 9y – z = 5 ⎧ x – 2y+ z = 0 ⎪ ⎨ y – 2z = 4 ⎪ ⎩ 4x + y+ 3z = 5 ⎧ x – 2y+ z = 0 [3]+(–4)[1] ⎪ ⎯ ⎯⎯ ⎯⎯ ⎯ → ⎨ y – 2z = 4 ⎪ ⎩ 9y– z = 5 6. 3(second) 3y+ 9z = 3 +(third) –3y+ 7z = 2 16z = 5 ⎧ x +6y – 4z =1 ⎧ x + 6y – 4z =1 ⎪ [3]+3[2] ⎪ ⎨ y +3z =1 ⎯ ⎯⎯ ⎯⎯ → ⎨ y +3z =1 ⎪ ⎩ –3y+ 7z = 2 ⎪ ⎩ 16z = 5 ⎡ 1 – 1 7. ⎢ ⎣ 0 21 43⎤ ⎦ ⎥ ⎯ ⎯⎯ [1]+12⎯⎯ [2]→ ⎣ ⎡ ⎢ 01 0154⎥⎤ ⎦ ⎡ 1 09⎤ 8. ⎢ 0 13⎥ ⎢ ⎥ ⎢ ⎣ 0 45⎦ ⎥ ⎡ 1 [3]+(–4)[2] ⎢ ⎯ ⎯⎯ ⎯⎯ ⎯ → 0 ⎢ ⎢ ⎣ 0 0 1 0 7 –2 16 9⎤ ⎥ 3 ⎥ –7⎥ ⎦ 17. Use [2] + 2[1] to change the –2 to a 0. 18. . Use [2] to change the 2 to a 1. 19. Use [1] to (–2)[2] to change the 2 to a 0. 20. Use [3] + (–4)[1] to change the 4 to a 0. 21. Interchange rows 1 and 2 or rows 1 and 3 to make the first entry in row 1 nonzero. ⎛ 1⎞ 22. Use ⎜ – ⎟ [2] to change the –3 to a 1. ⎝ 3⎠ 23. Use [1] + (–3)[3] to change the 3 to a 0. 24. Interchange rows 2 and 3 to make the second entry in row 2 nonzero. ⎡ 3 96⎤ 1 25. ⎢ ⎣ 2 86⎥ ⎦ ⎯ ⎯⎯ 3[1]→ ⎡ ⎢ ⎣ 21 38 26⎤ ⎥ ⎦ [2]+(–2)[1] ⎡ 1 3 2⎤ ⎯ ⎯⎯ ⎯⎯ ⎯ → ⎢ ⎣ 0 2 2⎥ ⎦ 12[2] ⎡ 1 3 2⎤ ⎯ ⎯⎯ → ⎢ ⎣ 0 1 1⎥ ⎦ [1]+(–3)[2] ⎡ 1 0 –1⎤ ⎯ ⎯⎯ ⎯⎯ ⎯ → ⎢ ⎣ 0 1 1⎥ ⎦ x = –1, y = 1 26. ⎢ ⎥ ⎡ 13 261⎤ ⎦ ⎯ ⎯⎯ 3[1]→ ⎡ ⎢ –21 –4663⎤ ⎥ ⎦ 28. ⎢ ⎢ ⎡ –4 –71 03–314⎥ ⎤ ⎥ ⎣ –2 –4⎣ [2]+2[1] ⎡ 1 6 3⎤ ⎢ ⎣ 6 14 750⎥ ⎦ ⎯ ⎯⎯ ⎯⎯ → ⎢ ⎣ 0 8 12⎥ ⎦ ⎡ 1 2 08⎤ 1[2] ⎡ 1 6 3⎤ ⎯ ⎯⎯ 2[1]→ ⎢ –4 –7 3–31⎥ 8⎢ ⎥ ⎯ ⎯⎯ → ⎢ ⎣ 0 1 32 ⎥ ⎦ ⎢ ⎣ 6 14 750⎥ ⎦ [1]+(–6)[2] ⎡ 1 0–6⎤ ⎡ 1 28⎤ ⎯ ⎯⎯ ⎯⎯ ⎯ → ⎢ ⎣ 0 132⎥ ⎦ ⎯ ⎯⎯ [2]+ 4[1]⎯⎯ → ⎢ ⎢ 0 11⎥ ⎥ x = –6, y = ⎢ ⎣ 6 1450⎥ ⎦ ⎡ 1 2 08⎤ [3]+(–6)[1] ⎢ ⎥ ⎡ 1 –3 41⎤ ⎯ ⎯⎯ ⎯⎯ ⎯ → ⎢ 0 1 31⎥ 27. ⎢ 4 –10 104⎥ ⎢ ⎣ 0 2 72⎥ ⎦ ⎢ ⎥ ⎢ ⎣ –3 9 −5–6⎥ ⎦ [1]+(–2)[2] ⎢ ⎡ 1 0 –66⎤ ⎥