Precalculus Student Solution Chapter 9

222 Chapter 9 Try It (−5, 3). 9.1. Not a solution. 9.2. The solution to the system is the ordered pair 9.3. (−2, −5) 9.4. (−6, −2) 9.5. (10, −4) 9.6. No solution. It is an inconsistent system. 9.7. The system is dependent so there are infinite solutions of the form (x, 2x + 5). 9.8. 700 children, 950 adults 9.9. (1, −1, 1) 9.10. No solution. 9.11. Infinite number of solutions of the form (x, 4x−11, −5x + 18). 9.12. ⎛ 1 1⎞ ⎝− 2 , 2 ⎠ (2, 8) and 9.13. (−1, 3) 9.14. {(1, 3), (1, −3), (−1, 3), (−1, −3)} 9.15. Shade the area bounded by the two curves, above the quadratic and below the line. 223 9.16. 3 − 2 x−3 x−2 9.17. 6 − 5 x−1 (x−1) 2 9.18. 3 + 2x−4 x−1 x 2 + 1 9.19. 2x + 1 x−2 + x 2 −2x + 3 ⎛x 2 −2x + 3⎞2 ⎝ ⎠ 9.20. (9.192) 6 + (−2) ⎤ ⎡ 5 4⎤ ⎡2 6 ⎤ ⎡ 3 −2⎤ ⎡ 2 + 3 A + B = ⎢1 0 ⎥ + ⎢ 1 5 ⎥ = ⎢ 1 + 1 0 + 5 ⎥ = ⎢ 2 5⎥ ⎣1 −3⎦ ⎣ −4 3⎦ ⎣1 + (−4) −3 + 3⎦ ⎣−3 0⎦ 9.21. ⎡−8 −2⎤ −2B = ⎣ −6 −4⎦ 9.22. | ⎡4 −3 11⎤ ⎣3 2 4 ⎦ 9.23. x − y + z=5 2x − y + 3z = 1 y + z = −9 9.24. (2, 1) 9.25. | ⎡ 1 − 5 5 17 ⎤ 2 2 2⎥ ⎢ ⎢ 0 1 5 9⎥ ⎣0 0 1 2⎦ 9.26. (1, 1, 1) 9.27. $150,000 at 7%, $750,000 at 8%, $600,000 at 10% 224 9.28. (9.308) 1(−4) + 4(1)⎤ ⎡1 ⎡ 1 4⎤⎡−3 −4⎤ ⎡ 1(−3) + 4(1) = AB = ⎣ = −1 −3⎦⎣ 1 1⎦ ⎣−1(−3) + −3(1) −1(−4) + −3(1)⎦ ⎣0 ⎡−3 −4⎤⎡ 1 4⎤ ⎡−3(1) + −4(−1) −3(4) + −4(−3)⎤ ⎡1 BA = ⎣ = = ⎦ ⎣ 1(4) + 1(−3)⎦ ⎣0 1 1 −1 −3⎦ ⎣ 1(1) + 1(−1) 9.29. A −1 9.30. ⎡ 3 ⎢ 5 =⎢ 2 ⎣− 5 0⎤ 1⎦ 0⎤ 1⎦ 1⎤ 5⎥ 1⎥ 5⎦ ⎡1 1 2 ⎤ A −1 = ⎢2 4 −3⎥ ⎣3 6 −5⎦ 9.31. ⎡4⎤ X = ⎢38⎥ ⎣58⎦ 9.32. (3, − 7) 9.33. −10 9.34. ⎛ 3 12 ⎞ ⎝−2, 5 , 5 ⎠ Section Exercises 1. No, you can either have zero, one, or infinitely many. Examine graphs. 3. This means there is no realistic break-even point. By the time the company produces one unit they are already making profit. 5. You can solve by substitution (isolating x or y ), graphically, or by addition. 7. Yes 9. Yes 11. (−1, 2) 13. (−3, 1) 15. ⎛ 3 ⎞ ⎝− 5 , 0⎠ 17. No solutions exist. 19. ⎛72 132 ⎞ ⎝5, 5 ⎠ 21. (6, −6) 23. ⎛ 1 1⎞ ⎝− 2 , 10 ⎠ 25. No solutions exist. 27. ⎛ 1 2⎞ ⎝− 5 , 3 ⎠ 225 29. ⎛ x + 3⎞ ⎝x, 2 ⎠ 31. (−4, 4) 33. ⎛1 1 ⎞ ⎝2 , 8 ⎠ 35. ⎛1 ⎞ ⎝6 , 0⎠ 37. ⎛ ⎝ x, 2(7x−6)⎞⎠ 39. ⎛ 5 4⎞ ⎝− 6 , 3 ⎠ 41. Consistent with one solution 43. Consistent with one solution 45. Dependent with infinitely many solutions 47. (−3.08, 4.91) 49. (−1.52, 2.29) 51. ⎛A + B A − B⎞ ⎝ 2 , 2 ⎠ 53. ⎛ −1 A ⎞ ⎝A − B, A − B⎠ 55. ⎛ CE − BF AF − CD ⎞ ⎝BD − AE , BD − AE ⎠ 57. They never turn a profit. 59. (1, 250, 100, 000) 61. The numbers are 7.5 and 20.5. 63. 24,000 65. 790 sophomores, 805 freshman 67. 56 men, 74 women 69. 10 gallons of 10% solution, 15 gallons of 60% solution 71. Swan Peak: $750,000, Riverside: $350,000 73. $12,500 in the first account, $10,500 in the second account. 75. High-tops: 45, Low-tops: 15 77. Infinitely many solutions. We need more information. 78. No, there can be only one, zero, or infinitely many solutions. 80. Not necessarily. There could be zero, one, or infinitely many solutions. For example, (0, 0, 0) is not a solution to the system below, but that does not mean that it has no solution. 2x + 3y−6z = 1 −4x−6y + 12z = −2 x + 2y + 5z = 10 82. Every system of equations can be solved graphically, by substitution, and by addition. However, systems of three equations become very complex to solve graphically so other methods are usually preferable. 84. No 86. Yes 88. (−1, 4, 2) 226 90. ⎛ 85 312 191 ⎞ ⎝− 107 , 107 , 107 ⎠ 92. ⎛ 1 ⎞ ⎝1, 2 , 0⎠ 94. (4, −6, 1) 96. ⎛ x + 28 ⎞ 1 ⎝x, 27 (65−16x), 27 ⎠ 98. ⎛ 45 17 ⎞ ⎝− 13 , 13 , −2⎠ 100. No solutions exist 102. (0, 0, 0) 104. ⎛4 3⎞ 1 ⎝7 , − 7 , − 7 ⎠ 106. (7, 20, 16) 108. (−6, 2, 1) 110. (5, 12, 15) 112. (−5, −5, −5) 114. (10, 10, 10) 116. ⎛1 1 4 ⎞ ⎝2 , 5 , 5 ⎠ 118. ⎛1 2 4 ⎞ ⎝2 , 5 , 5 ⎠ 120. (2, 0, 0) 122. (1, 1, 1) 124. 128 , 23 , 28 ⎛557 557 557 ⎞ ⎝ ⎠ 126. (6, −1, 0) 128. 24, 36, 48 130. 70 grandparents, 140 parents, 190 children 132. Your share was $19.95, Sarah’s share was $40, and your other roommate’s share was $22.05. 134. There are infinitely many solutions; we need more information 136. 500 students, 225 children, and 450 adults 138. The BMW was $49,636, the Jeep was $42,636, and the Toyota was $47,727. 140. $400,000 in the account that pays 3% interest, $500,000 in the account that pays 4% interest, and $100,000 in the account that pays 2% interest. 142. The United States consumed 26.3%, Japan 7.1%, and China 6.4% of the world’s oil. 144. Saudi Arabia imported 16.8%, Canada imported 15.1%, and Mexico 15.0% 146. Birds were 19.3%, fish were 18.6%, and mammals were 17.1% of endangered species 227 148. A nonlinear system could be representative of two circles that overlap and intersect in two locations, hence two solutions. A nonlinear system could be representative of a parabola and a circle, where the vertex of the parabola meets the circle and the branches also intersect the circle, hence three solutions. 150. No. There does not need to be a feasible region. Consider a system that is bounded by two parallel lines. One inequality represents the region above the upper line; the other represents the region below the lower line. In this case, no points in the plane are located in both regions; hence there is no feasible region. 152. Choose any number between each solution and plug into C(x) and R(x). If C(x) < R(x), then there is profit. 154. (0, −3), (3, 0) 156. ⎛ 3 2 3 2 ⎞ ⎛3 2 3 2⎞ ⎝− 2 , 2 ⎠, ⎝ 2 , − 2 ⎠ 158. (−3, 0), (3, 0) 160. ⎛1 62 ⎞ ⎛1 62 ⎞ ⎝4 , − 8 ⎠, ⎝4 , 8 ⎠ 162. ⎛ 398 199 ⎞ ⎛ 398 199 ⎞ ⎝− 4 , 4 ⎠, ⎝ 4 , 4 ⎠ 164. (0, 2), (1, 3) 166. ⎛ 1⎛ ⎞⎞ ⎛ 1 ⎛ ⎞⎞ ⎞ 1⎛ ⎞ 1⎛ ⎝− 2 ⎝ 5−1⎠, 2 ⎝1 − 5⎠⎠, ⎝ 2 ⎝ 5−1⎠, 2 ⎝1 − 5⎠⎠ 168. (5, 0) 170. (0, 0) 172. (3, 0) 174. No Solutions Exist 176. No Solutions Exist 178. ⎛ 2 2⎞ ⎛ 2 2⎞ ⎛ 2 2⎞ ⎛ 2 2⎞ ⎝− 2 , − 2 ⎠, ⎝− 2 , 2 ⎠, ⎝ 2 , − 2 ⎠, ⎝ 2 , 2 ⎠ 180. (2, 0) 182. ⎛ ⎝ − 7, −3⎞⎠, ⎛⎝− 7, 3⎞⎠, 184. ⎛ ⎝ 7, −3⎞⎠, ⎛ ⎝ 7, 3⎞⎠ ⎛ 1⎛ ⎞ 1⎛ ⎞⎞ ⎛ 1 ⎛ ⎞ 1⎛ ⎞⎞ ⎝− 2 ⎝ 73−5⎠, 2 ⎝7 − 73⎠⎠, ⎝ 2 ⎝ 73−5⎠, 2 ⎝7 − 73⎠⎠ 186. 228 188. 190. 192. 229 194. 196. ⎛ 70 70 35 ⎞ ⎛ 35 ⎞ ⎛ 70 35 ⎞ ⎛ 70 35 ⎞ ⎝−2 383 , −2 29 ⎠, ⎝−2 383 , 2 29 ⎠, ⎝2 383 , −2 29 ⎠, ⎝2 383 , 2 29 ⎠ 198. No Solution Exists 200. x = 0, y > 0 and 0 < x < 1, x < y < 1x 202. 12, 288 204. 2–20 computers 206. No, a quotient of polynomials can only be decomposed if the denominator can be factored. For example, 1 x 2 + 1 cannot be decomposed because the denominator cannot be factored. 208. Graph both sides and ensure they are equal. 210. If we choose x = −1, then the B-term disappears, letting us immediately know that A = 3. We could alternatively plug in x = − 5, 3 giving us a B-value of −2. 212. 8 − 5 x + 3 x−8 214. 1 + 9 x+5 x+2 216. 3 + 4 5x−2 4x−1 230 218. 5 + 5 2(x + 3) 2(x−3) 220. 3 + 3 x + 2 x−2 222. 9 + 11 5(x + 2) 5(x−3) 224. 8 − 5 x−3 x−2 226. 1 + 2 x−2 (x−2) 2 228. − 6 + 3 4x + 5 (4x + 5) 2 230. − 1 − 2 2 x−7 (x−7) 232. 3 4− x 2(x + 1) + 7 2(x + 1) 2 234. 7 4+ 2 − 3 + x x 2 3x + 2 2(3x + 2) 2 236. x+1 + 3 x2 + x + 3 x + 2 238. 4−3x + 1 x 2 + 3x + 8 x−1 240. 2x−1 + 2 x 2 + 6x + 1 x + 3 242. 1 + 4 x 2 + x + 1 x−1 244. 2 + 3 x 2 −3x + 9 x + 3 246. − 1 + 1 4x 2 + 6x + 9 2x−3 248. 4x 1+ 1 − x x+6 x 2 −6x + 36 250. x + 6 + 4x + 3 x 2 + 1 ⎛x 2 + 1⎞2 ⎝ ⎠ 252. x + 1 + 2x + 3 x + 2 (x + 2) 2 231 254. 3x 1 − x 2 + 3x + 25 ⎛x 2 + 3x + 25⎞2 ⎝ 256. x 1 − + 8x 8⎛x 2 + 4⎞ ⎝ ⎠ ⎠ 10 − x 2⎛⎝x 2 + 4⎞⎠ 2 258. 9 16 7 − 16 x − 2 + x−1 − (x−1) 2 x 260. 5 1 − 2 + x + 1 (x + 1) 2 (x + 1) 3 262. 5 − 3 7 + 7 − x−2 10(x + 2) x + 8 10(x−8) 264. 5 5 −5 − + 11 + 4x 2(x + 2) 2(x + 4) 4(x + 4) 265. No, they must have the same dimensions. An example would include two matrices of different dimensions. One cannot add the following two matrices because the first is a 2×2 matrix and the second is a 2×3 matrix. ⎡1 2⎤ ⎡6 5 4⎤ ⎣3 4⎦ + ⎣3 2 1⎦ has no sum. 267. Yes, if the dimensions of A are m×n and the dimensions of B are n×m, both products will be defined. 269. Not necessarily. To find AB, we multiply the first row of A by the first column of B to get the first entry of AB. To find BA, we multiply the first row of B by the first column of A to get the first entry of BA. Thus, if those are unequal, then the matrix multiplication does not commute. 271. ⎡11 19⎤ ⎢15 94⎥ ⎣17 67⎦ 273. ⎡−4 2⎤ ⎣ 8 1⎦ 275. Undidentified; dimensions do not match 277. ⎡ 9 27 ⎤ ⎢63 36 ⎥ ⎣ 0 192⎦ 279. ⎡ −64 −12 −28 −72 ⎤ ⎣−360 −20 −12 −116⎦ 232 281. ⎡ 1, 800 1, 200 1, 300⎤ ⎥ ⎢ ⎢ 800 1, 400 600 ⎥ ⎣ 700 400 2, 100⎦ 283. ⎡20 102⎤ ⎣28 28 ⎦ 285. ⎡ 60 41 2 ⎤ ⎣−16 120 −216⎦ 287. ⎡−68 24 136⎤ ⎢−54 −12 64 ⎥ ⎣−57 30 128⎦ 289. Undefined; dimensions do not match. 291. ⎡−8 41 −3 ⎤ ⎢ 40 −15 −14⎥ ⎣ 4 27 42 ⎦ 293. ⎡−840 650 −530⎤ ⎢ 330 360 250 ⎥ ⎣ −10 900 110 ⎦ 295. ⎡−350 1, 050⎤ ⎣ 350 350 ⎦ 297. Undefined; inner dimensions do not match. 299. ⎡ 1, 400 700⎤ ⎣−1, 400 700⎦ 301. ⎡ 332, 500 927, 500⎤ ⎣−227, 500 87, 500 ⎦ 303. 0 ⎡490, 000 ⎤ ⎣ 0 490, 000⎦ 305. ⎡−2 3 4 ⎤ ⎣−7 9 −7⎦ 307. ⎡ −4 29 21⎤ ⎣−27 −3 1 ⎦ 309. ⎡ −3 −2 −2⎤ ⎢−28 59 46 ⎥ ⎣ −4 16 7 ⎦ 311. ⎡ 1 −18 −9 ⎤ ⎢−198 505 369⎥ ⎣ −72 126 91 ⎦ 313. ⎡0 1.6⎤ ⎣9 −1 ⎦ 233 315. ⎡ 2 24 −4.5⎤ ⎢ 12 32 −9 ⎥ ⎣−8 64 61 ⎦ 317. ⎡0.5 3 0.5⎤ ⎢2 1 2⎥ ⎣ 10 7 10 ⎦ 319. ⎡1 0 0⎤ ⎢0 1 0⎥ ⎣0 0 1⎦ 321. ⎡1 0 0⎤ ⎢0 1 0⎥ ⎣0 0 1⎦ 323. ⎧⎡1 ⎪⎢0 ⎪⎣ 0 Bn = ⎨ ⎪⎡1 ⎪⎢0 ⎩⎣0 0⎤ 0⎥, 1⎦ 0⎤ 1⎥, 0⎦ 0 1 0 0 0 1 n even, n odd. 324. Yes. For each row, the coefficients of the variables are written across the corresponding row, and a vertical bar is placed; then the constants are placed to the right of the vertical bar. 326. No, there are numerous correct methods of using row operations on a matrix. Two possible ways are the following: (1) Interchange rows 1 and 2. Then R 2 = R 2 −9R 1. (2) R 2 = R 1 −9R 2. Then divide row 1 by 9. 328. No. A matrix with 0 entries for an entire row would have either zero or infinitely many solutions. 330. ⎡ ⎢0 16 ⎢ ⎣ 9 −1 332. ⎡ ⎢ ⎢ 1 ⎢ ⎢ ⎢ ⎢ ⎢ ⎢12 ⎢ ⎢ ⎣ 3 334. | ⎤ 4⎥ ⎥ ⎦ 2 5 8 3 0 4 9 | −2x + 5y = 5 6x−18y = 26 ⎤ ⎥ 16⎥ ⎥ ⎥ ⎥ ⎥ ⎥ 4⎥ ⎥ ⎥ ⎦ −7 234 336. 3x + 2y = 13 −x−9y + 4z = 53 8x + 5y + 7z = 80 338. 4x + 5y−2z = 12 y + 58z = 2 8x + 7y−3z = −5 340. No solutions 342. (−1, −2) 344. (6, 7) 346. (3, 2) 348. ⎛1 1 ⎞ ⎝5 , 2 ⎠ 350. ⎞ ⎛ 4 ⎝x, 15 (5x + 1)⎠ 352. (3, 4) 354. ⎛196 5⎞ ⎝ 39 , − 13 ⎠ 356. (31, −42, 87) 358. ⎛21 1 9 ⎞ ⎝40 , 20 , 8 ⎠ 360. ⎛18 15 15 ⎞ ⎝13 , 13 , − 13 ⎠ 362. ⎛ ⎞ 1 ⎝x, y, 2 (1−2x−3y)⎠ 364. ⎛ ⎞ x ⎝x, − 2 , −1⎠ 366. (125, −25, 0) 368. (8, 1, −2) 370. (1, 2, 3) 372. ⎛ 31 3x 1 ⎞ ⎝x, 28 − 4 , 28 (−7x−3)⎠ 374. No solutions exist. 376. 860 red velvet, 1,340 chocolate 378. 4% for account 1, 6% for account 2 380. $126 382. Banana was 3%, pumpkin was 7%, and rocky road was 2% 384. 100 almonds, 200 cashews, 600 pistachios 235 385. If A −1 is the inverse of A, then AA −1 = I, the identity matrix. Since A is also the inverse of A −1, A −1 A = I. You can also check by proving this for a 2×2 matrix. 387. No, because ad and bc are both 0, so ad − bc = 0, which requires us to divide by 0 in the formula. 389. Yes. Consider the matrix ⎡0 1⎤ ⎣1 0⎦. The inverse is found with the following calculation: ⎡ 0 −1⎤ ⎡0 1⎤ −1 1 A = = . 0(0)−1(1) ⎣−1 0 ⎦ ⎣1 0⎦ 391. ⎡1 0⎤ AB = BA = ⎣ ⎦ = I 0 1 393. ⎡1 0⎤ AB = BA = ⎣ ⎦ = I 0 1 395. ⎡1 0 0⎤ AB = BA = ⎢0 1 0⎥ = I ⎣0 0 1⎦ 397. 1 ⎡ 9 2⎤ 29 ⎣−1 3⎦ 399. 1 ⎡−2 7⎤ 69 ⎣ 9 3⎦ 401. There is no inverse 403. 4 ⎡0.5 1.5 ⎤ 7 ⎣ 1 −0.5⎦ 405. ⎡−5 5 −3⎤ 1 ⎢ 20 −3 12 ⎥ 17 ⎣ 1 −1 4 ⎦ 407. ⎡ 47 −57 69 ⎤ 1 ⎢ 10 19 −12⎥ 209 ⎣ −24 38 −13⎦ 409. ⎡ 18 60 −168⎤ ⎢−56 −140 448 ⎥ ⎣ 40 80 −280⎦ 411. (−5, 6) 413. (2, 0) 236 415. ⎛1 5⎞ ⎝3 , − 2 ⎠ 417. ⎛ 2 11 ⎞ ⎝− 3 , − 6 ⎠ 419. ⎛ 1 1⎞ ⎝7, 2 , 5 ⎠ 421. (5, 0, −1) 423. 1 (−35, −97, −154) 34 425. 1 (65, −1136, −229) 690 427. ⎛ 37 8 ⎞ ⎝− 30 , 15 ⎠ 429. ⎛ 10 2⎞ ⎝123 , −1, 5 ⎠ 431. ⎡2 1 −1 −1⎤ 1 ⎢0 1 1 −1⎥ 2 ⎢0 −1 1 1⎥ ⎣0 1 −1 1⎦ 433. 2 1 −7⎤ ⎡ 3 1 ⎢ 18 −53 32 10⎥ 39 ⎢ 24 −36 21 9⎥ ⎣−9 46 −16 −5⎦ 435. ⎡ 1 0 0 0 0 ⎢ 0 1 0 0 0 ⎢ ⎢ 0 0 1 0 0 ⎢ 0 0 0 1 0 ⎢ 0 0 0 0 1 ⎣−1 −1 −1 −1 −1 0⎤ 0⎥ ⎥ 0⎥ 0⎥ 0⎥ 1⎦ 437. Infinite solutions. 439. 50% oranges, 25% bananas, 20% apples 441. 10 straw hats, 50 beanies, 40 cowboy hats 443. Tom ate 6, Joe ate 3, and Albert ate 3. 445. 124 oranges, 10 lemons, 8 pomegranates 446. A determinant is the sum and products of the entries in the matrix, so you can always evaluate that product—even if it does end up being 0. 448. The inverse does not exist. 450. −2 452. 7 454. −4 456. 0 237 458. −7, 990.7 460. 3 462. −1 464. 224 466. 15 468. −17.03 470. (1, 1) 472. ⎛1 1 ⎞ ⎝2 , 3 ⎠ 474. (2, 5) 476. ⎛ 1⎞ ⎝−1, − 3 ⎠ 478. (15, 12) 480. (1, 3, 2) 482. (−1, 0, 3) 484. ⎛1 ⎞ ⎝2 , 1, 2⎠ 486. (2, 1, 4) 488. Infinite solutions 490. 24 492. 1 494. Yes; 18, 38 496. Yes; 33, 36, 37 498. $7,000 in first account, $3,000 in second account. 500. 120 children, 1,080 adult 502. 4 gal yellow, 6 gal blue 504. 13 green tomatoes, 17 red tomatoes 506. Strawberries 18%, oranges 9%, kiwi 10% 508. 100 for movie 1, 230 for movie 2, 312 for movie 3 510. 20–29: 2,100, 30–39: 2,600, 40–49: 825 512. 300 almonds, 400 cranberries, 300 cashews Review Exercises 514. No 516. (−2, 3) 518. (4, − 1) 520. No solutions exist. 238 522. (300, 60, 000) 523. (400, 30, 000) 524. (10, − 10, 10) 526. No solutions exist. 528. (−1, − 2, 3) 530. ⎛ 8x 14x ⎞ ⎝x, 5 , 5 ⎠ 532. 11, 17, 33 534. (2, − 3), (3, 2) 536. No solution 538. No solution 540. 542. 544. 2 , −4 x+2 x+1 546. 7 , −15 x + 5 (x + 5) 2 548. 3 , −4x + 1 x − 5 x 2 + 5x + 25 239 550. x − 4 , 5x + 3 (x 2 − 2) (x 2 − 2) 2 552. ⎡−16 8 ⎤ ⎣ −4 −12⎦ 554. undefined; dimensions do not match 556. undefined; inner dimensions do not match 558. ⎡113 28 10 ⎤ ⎢ 44 81 −41⎥ ⎣ 84 98 −42⎦ 560. ⎡−127 −74 176⎤ ⎢ −2 11 40 ⎥ ⎣ 28 77 38 ⎦ 562. undefined; inner dimensions do not match 564. x − 3z = 7 y + 2z = − 5 566. 2 1 ⎡−2 ⎢ 2 −8 5 ⎣ 19 −10 22 568. ⎡ 1 0 3 ⎢−1 4 0 ⎣ 0 1 2 | with infinite solutions | 7⎤ 0⎥ 3⎦ 12⎤ 0⎥ −7⎦ 570. No solutions exist. 572. No solutions exist. 574. 1 ⎡2 7⎤ 8 ⎣6 1⎦ 576. No inverse exists. 578. (−20, 40) 580. (−1, 0.2, 0.3) 582. 17% oranges, 34% bananas, 39% apples 584. 0 586. 6 588. ⎛ 1⎞ ⎝6, 2 ⎠ 590. (x, 5x + 3) 592. ⎛ 1⎞ ⎝0, 0, − 2 ⎠ Practice Test 594. Yes 596. No solutions exist. 598. 1 (10, 5, 4) 20 240 600. ⎛ 16x 13x ⎞ ⎝x, 5 − 5 ⎠ 602. ( − 2 2, − 17), ⎛⎝−2 2, 17⎞⎠, ⎛⎝2 2, − 17⎞⎠, ⎛⎝2 2, 17⎞⎠ 604. 606. 5 − 2x + 3 3x + 1 (3x + 1) 2 608. ⎡ 17 51⎤ ⎣−8 11⎦ 610. ⎡ 12 −20⎤ ⎣−15 30 ⎦ 612. −1 8 614. ⎡ 14 −2 13 ⎢−2 3 −6 ⎣ 1 −5 12 | 140⎤ −1⎥ 11⎦ 616. No solutions exist. 618. (100, 90) 620. ⎛ 1 ⎞ ⎝100 , 0⎠ 622. 32 or more cell phones per day