# ER596Chapter 8Matrices and DeterminantsEncoding a Message In Exercises 47 and 4the uncoded 1 x 3 row matrices for the message(b) encode the message using the encoding matTesting forExercises 23-28, useCollinear Points Ina determinant todetermine whether the points are collinear.Encoding(23. (2,-6), (0, - 2), (3, - 8)24. (3, -5), (6, 1), (4, 2)25. (2, -), (-4, 4), (6, – 3)26. (0, 1), (–2, 3). (1, – )Message47. CALL ME TOMORROW9.427. (0, 2), (1, 2.4), (–1, 1.6)-348. PLEASE SEND MONEY28. (3, 7), (4, 9.5), (– 1, –5)Finding a Coordinate In Exercises 29 and 30, findthe value of y such that the points are collinear.Encoding a Message In Exercises 49.cryptogram for the message using the matri29. (2, – 5), (4, y), (5, -2) 30. (-6, 2), (- 5, y), (-3, 5)9.Finding an Equation of a Line InExercises 31–36, use a determinant to findan equation of the line passing through thepoints.-4 -7-149. LANDING SUCCESSFUL50. ICEBERG DEAD AHEAD31. (0, 0), (5, 3)32. (0, 0), (– 2, 2)34. (10, 7), (-2,-7)36. (, 4), (6, 12)51. HAPPY BIRTHDAY33. (-4, 3), (2, 1)35. (-, 3). (§, 1)52. OPERATION OVERLOADDecoding a Message In Euse A-1 to decode the cryptogTransforming a Square In Exercises37-40, use matrices to find the vertices of theimage of the square with the given verticesafter the given transformation. Then sketchthe square and its image.:-1.53. A3%3D11 21 64 112 25 50 29 5337. (0, 0), (0, 3), (3, 0), (3, 3); horizontal stretch, k = 275 55 9238. (1, 2), (3, 2), (1, 4), (3, 4); reflection in the x-axis[254. A =339. (4, 3), (5, 3), (4, 4), (5, 4); reflection in the y-axis%3D4.:-40. (1, 1), (3, 2), (0, 3), (2, 4); vertical shrink, k85 120 6 8 10 15 84 117Finding the Area of a Parallelogram IaExercises 41-44, use a determinant to Gdthe area of the parallelogram with the given125 60 80 30 45 19 2610.55. A =1.-1vertices.3.-1 -9 3841. (0, 0), (1, 0), (2, 2), (3, 2)9.-19-19 2842. (0, 0), (3, 0), (4, 1), (7, 1)-80 25 41 -64 21 31943. (0, 0), (–2, 0), (3, 5), (1, 5)2-444. (0, 0), (0, 8), (8, –6), (8, 2)56. A =0.13]4 -5Encoding a Message In Exercises 45and 46, (a) write the uncoded 1 x 2 rowmatrices for the message, and then (b) encodethe message using the encoding matrix.112 - 140 83 19 -25 13- 118 71 20 21 38 35 -23Decoding a Message In Exercise:the cryptogram by using the inverse49-52.MessageEncoding Matrix45. COME HOME SOON57. 20 17 -15 -12 -56 -103 562 143 18146. HELP IS ON THE WAY2 358. 13 -9 -59 6110611123.EC15бк.OK+EXACTI

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We first have to set up a determinant using x,y and the given points and set it equal to 0, as: ...

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