Explanation Given: The given matrix A is, A = [ -5 4 -3 10 -7 6 8 -6 5 ] The given code is, 145 − 105 92 264 − 188 160 23 − 16 15 129 − 84 78 − 9 8 − 5 159 − 118 100 219 − 152 133 370 − 265 255 − 105 84 − 63 Approach: A cryptogram is a message written according to a secret code. (The Greek word kryptos means “hidden.”) Matrix multiplication can be used to encode and decode messages. To begin, assign a number to each letter in the alphabet (with 0 assigned to a blank space), as listed below, 0 = _ 9 = I 18 = R 1 = A 10 = J 19 = S 2 = B 11 = K 20 = T 3 = C 12 = L 21 = U 4 = D 13 = M 22 = V 5 = E 14 = N 23 = W 6 = F 15 = O 24 = X 7 = G 16 = P 25 = Y 8 = H 17 = Q 26 = Z Then convert the message to number and partition the number into uncoded row matrices, each having n entities. The general 3 × 3 matrix is given as, A = [ a 11 a 12 a 13 a 21 a 22 a 23 a 31 a 32 a 33 ] Then, the adjoint of the matrix A is given as, Finally A − 1 is calculated with the of the formula, A − 1 = 1 | A | ( a d j A ) ... ( 1 ) Calculation: Consider the given matrix A , A = [ -5 4 -3 10 -7 6 8 -6 5 ] The determinant of A is given as, | A | = | − 5 4 − 3 10 − 7 6 8 − 6 5 | = ( − 5 ) | − 7 6 − 6 5 | − ( 4 ) | 10 6 8 5 | + ( − 3 ) | 10 − 7 8 − 6 | = − 5 ( − 35 + 36 ) − 4 ( 50 − 48 ) − 3 ( − 60 + 56 ) = − 5 ( 1 ) − 4 ( 2 ) − 3 ( − 4 ) Further solve the above equation. | A | = − 5 − 8 + 12 = − 13 + 12 = − 1 Since, | A | ≠ 0 . So, A − 1 exists. The value of adjoint A is, a d j A = [ + | − 7 6 − 6 5 | − | 10 6 8 5 | + | 10 − 7 8 − 6 | − | 4 − 3 − 6 5 | + | − 5 − 3 8 5 | − | − 5 4 8 − 6 | + | 4 − 3 − 7 6 | − | − 5 − 3 10 6 | + | − 5 4 10 − 7 | ] T = [ 1 − 2 − 4 − 2 − 1 2 3 0 − 5 ] T = [ 1 − 2 3 − 2 − 1 0 − 4 2 − 5 ] So, the value of A − 1 is given as,

Bundle: Precalculus, Loose-leaf Version, 10th + WebAssign Printed Access Card for Larson's Precalculus, 10th Edition, Single-Term

10th Edition

ISBN: 9781337605090

Author: Ron Larson

Publisher: Cengage Learning

See similar textbooks

Videos

Question

Chapter 8.CR, Problem 122CR

To determine

The decoded cryptogram based on the inverse of the given matrix A=[-54-310-768-65].

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 8.CR, Problem 121CR

Chapter 8.CR, Problem 123CR

Students have asked these similar questions

On from the equation: 2 u = C₁ + C₂ Y + Czy + Cu y³ Find C₁, C₂, C3 and Cy Using these following Cases : (a) 4=0 at y=0 (b) U = U∞ at y = 8 du (c) at Y = S ду --y. ди = 0 at y = 0 буг

Tips S ps L 50. lim x2 - 4 x-2x+2 51. lim 22 - X 52. 53. x 0 Answer lim x 0 lim 2-5 X 2x2 2 x² Answer -> 54. lim T - 3x - - 25 +5 b+1 b3b+3 55. lim X x-1 x 1 Answer 56. lim x+2 x 2 x 2 57. lim x²-x-6 x-2 x²+x-2 Answer-> 23-8 58. lim 2-22-2

S 36. lim 5x+2 x-2 37. lim √√2x4 + x² x-3 Answer-> 2x3 +4 38. lim x12 √ x² + 1 √√x² + 8 39. lim x-1 2x+4 Answer 40. lim x3 2x x√x² + 7 √√2x+3

Chapter 8 Solutions

Bundle: Precalculus, Loose-leaf Version, 10th + WebAssign Printed Access Card for Larson's Precalculus, 10th Edition, Single-Term

Ch. 8.1 - Prob. 1CP Ch. 8.1 - Prob. 2CP Ch. 8.1 - Prob. 3CP Ch. 8.1 - Prob. 4CP Ch. 8.1 - Prob. 5CP Ch. 8.1 - Prob. 6CP Ch. 8.1 - Prob. 7CP Ch. 8.1 - Prob. 8CP Ch. 8.1 - Prob. 9CP Ch. 8.1 - Prob. 1E

Knowledge Booster

$Calculus$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.

The decoded cryptogram based on the inverse of the given matrix A = [ -5 4 -3 10 -7 6 8 -6 5 ] .

Solution Summary: The author explains how matrix multiplication can be used to encode and decode messages.

Videos

The decoded cryptogram based on the inverse of the given matrix A=[-54-310-768-65].

Want to see the full answer?

Chapter 8 Solutions