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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ER
596
Chapter 8
Matrices and Determinants
Encoding a Message In Exercises 47 and 4
the uncoded 1 x 3 row matrices for the message
(b) encode the message using the encoding mat
Testing for
Exercises 23-28, use
Collinear Points In
a determinant to
determine 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, – )
Message
47. CALL ME TOMORROW
9.
4
27. (0, 2), (1, 2.4), (–1, 1.6)
-3
48. PLEASE SEND MONEY
28. (3, 7), (4, 9.5), (– 1, –5)
Finding a Coordinate In Exercises 29 and 30, find
the value of y such that the points are collinear.
Encoding a Message In Exercises 49.
cryptogram for the message using the matri
29. (2, – 5), (4, y), (5, -2) 30. (-6, 2), (- 5, y), (-3, 5)
9.
Finding an Equation of a Line In
Exercises 31–36, use a determinant to find
an equation of the line passing through the
points.
-4 -7
-1
49. LANDING SUCCESSFUL
50. ICEBERG DEAD AHEAD
31. (0, 0), (5, 3)
32. (0, 0), (– 2, 2)
34. (10, 7), (-2,-7)
36. (, 4), (6, 12)
51. HAPPY BIRTHDAY
33. (-4, 3), (2, 1)
35. (-, 3). (§, 1)
52. OPERATION OVERLOAD
Decoding a Message In E
use A-1 to decode the cryptog
Transforming a Square In Exercises
37-40, use matrices to find the vertices of the
image of the square with the given vertices
after the given transformation. Then sketch
the square and its image.
:-
1.
53. A
3
%3D
11 21 64 112 25 50 29 53
37. (0, 0), (0, 3), (3, 0), (3, 3); horizontal stretch, k = 2
75 55 92
38. (1, 2), (3, 2), (1, 4), (3, 4); reflection in the x-axis
[2
54. A =
3
39. (4, 3), (5, 3), (4, 4), (5, 4); reflection in the y-axis
%3D
4.
:-
40. (1, 1), (3, 2), (0, 3), (2, 4); vertical shrink, k
85 120 6 8 10 15 84 117
Finding the Area of a Parallelogram Ia
Exercises 41-44, use a determinant to Gd
the area of the parallelogram with the given
125 60 80 30 45 19 26
1
0.
55. A =
1.
-1
vertices.
3.
-1 -9 38
41. (0, 0), (1, 0), (2, 2), (3, 2)
9.
-19
-19 28
42. (0, 0), (3, 0), (4, 1), (7, 1)
-80 25 41 -64 21 319
43. (0, 0), (–2, 0), (3, 5), (1, 5)
2
-4
44. (0, 0), (0, 8), (8, –6), (8, 2)
56. A =
0.
1
3]
4 -5
Encoding a Message In Exercises 45
and 46, (a) write the uncoded 1 x 2 row
matrices for the message, and then (b) encode
the message using the encoding matrix.
112 - 140 83 19 -25 13
- 118 71 20 21 38 35 -23
Decoding a Message In Exercise:
the cryptogram by using the inverse
49-52.
Message
Encoding Matrix
45. COME HOME SOON
57. 20 17 -15 -12 -56 -10
3 5
62 143 181
46. HELP IS ON THE WAY
2 3
58. 13 -9 -59 61
106
1
112
3.
EC
15
бк.
OK+
EXA
CTI
help_outline

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ER 596 Chapter 8 Matrices and Determinants Encoding a Message In Exercises 47 and 4 the uncoded 1 x 3 row matrices for the message (b) encode the message using the encoding mat Testing for Exercises 23-28, use Collinear Points In a determinant to determine 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, – ) Message 47. CALL ME TOMORROW 9. 4 27. (0, 2), (1, 2.4), (–1, 1.6) -3 48. PLEASE SEND MONEY 28. (3, 7), (4, 9.5), (– 1, –5) Finding a Coordinate In Exercises 29 and 30, find the value of y such that the points are collinear. Encoding a Message In Exercises 49. cryptogram for the message using the matri 29. (2, – 5), (4, y), (5, -2) 30. (-6, 2), (- 5, y), (-3, 5) 9. Finding an Equation of a Line In Exercises 31–36, use a determinant to find an equation of the line passing through the points. -4 -7 -1 49. LANDING SUCCESSFUL 50. ICEBERG DEAD AHEAD 31. (0, 0), (5, 3) 32. (0, 0), (– 2, 2) 34. (10, 7), (-2,-7) 36. (, 4), (6, 12) 51. HAPPY BIRTHDAY 33. (-4, 3), (2, 1) 35. (-, 3). (§, 1) 52. OPERATION OVERLOAD Decoding a Message In E use A-1 to decode the cryptog Transforming a Square In Exercises 37-40, use matrices to find the vertices of the image of the square with the given vertices after the given transformation. Then sketch the square and its image. :- 1. 53. A 3 %3D 11 21 64 112 25 50 29 53 37. (0, 0), (0, 3), (3, 0), (3, 3); horizontal stretch, k = 2 75 55 92 38. (1, 2), (3, 2), (1, 4), (3, 4); reflection in the x-axis [2 54. A = 3 39. (4, 3), (5, 3), (4, 4), (5, 4); reflection in the y-axis %3D 4. :- 40. (1, 1), (3, 2), (0, 3), (2, 4); vertical shrink, k 85 120 6 8 10 15 84 117 Finding the Area of a Parallelogram Ia Exercises 41-44, use a determinant to Gd the area of the parallelogram with the given 125 60 80 30 45 19 26 1 0. 55. A = 1. -1 vertices. 3. -1 -9 38 41. (0, 0), (1, 0), (2, 2), (3, 2) 9. -19 -19 28 42. (0, 0), (3, 0), (4, 1), (7, 1) -80 25 41 -64 21 319 43. (0, 0), (–2, 0), (3, 5), (1, 5) 2 -4 44. (0, 0), (0, 8), (8, –6), (8, 2) 56. A = 0. 1 3] 4 -5 Encoding a Message In Exercises 45 and 46, (a) write the uncoded 1 x 2 row matrices for the message, and then (b) encode the message using the encoding matrix. 112 - 140 83 19 -25 13 - 118 71 20 21 38 35 -23 Decoding a Message In Exercise: the cryptogram by using the inverse 49-52. Message Encoding Matrix 45. COME HOME SOON 57. 20 17 -15 -12 -56 -10 3 5 62 143 181 46. HELP IS ON THE WAY 2 3 58. 13 -9 -59 61 106 1 112 3. EC 15 бк. OK+ EXA CTI

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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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