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
Inverse Normal Distribution
The method used for finding the corresponding z-critical value in a normal distribution using the known probability is said to be an inverse normal distribution. The inverse normal distribution is a continuous probability distribution with a family of two parameters.
Mean, Median, Mode
It is a descriptive summary of a data set. It can be defined by using some of the measures. The central tendencies do not provide information regarding individual data from the dataset. However, they give a summary of the data set. The central tendency or measure of central tendency is a central or typical value for a probability distribution.
Z-Scores
A z-score is a unit of measurement used in statistics to describe the position of a raw score in terms of its distance from the mean, measured with reference to standard deviation from the mean. Z-scores are useful in statistics because they allow comparison between two scores that belong to different normal distributions.
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