Concept explainers
The cryptogram decoding by using inverse of A.

Answer to Problem 58E
The message is
Explanation of Solution
Given information:
Formula used:
The elementary row operations is
Calculation:
Consider the encoding matrix:
The inverse of this matrix is the decoding matrix.
To find the inverse of this matrix, begin by adjoining the identity matrix to this matrix as:
Use elementary row operations to obtain the form
So, the matrix A is invertible and its inverse is:
Partition the coded messages into groups of three.
Thus, the coded row matrices will be,
Multiply each coded row matrix by
Thus,
Coded Matrix Decoding Matrix Uncoded Matrix
So, the uncoded row matrices are:
Finally, removing the matrix notation:
Thus, the message is:
Conclusion:
The message is
Chapter 8 Solutions
EBK PRECALCULUS W/LIMITS
- Find the point of diminishing returns (x,y) for the function R(X), where R(x) represents revenue (in thousands of dollars) and x represents the amount spent on advertising (in thousands of dollars). R(x) = 10,000-x3 + 42x² + 700x, 0≤x≤20arrow_forwardDifferentiate the following functions. (a) y(x) = x³+6x² -3x+1 (b) f(x)=5x-3x (c) h(x) = sin(2x2)arrow_forwardx-4 For the function f(x): find f'(x), the third derivative of f, and f(4) (x), the fourth derivative of f. x+7arrow_forward
- In x For the function f(x) = find f'(x). Then find f''(0) and f''(9). 11x'arrow_forwardLet f(x) = √√x+3 and g(x) = 6x − 2. Find each of the following composite functions and state the domain: (a) fog (b) gof, (c) fof (d) gogarrow_forwardCompute the following: (a) 8x³ + 3x dx (b) cos(2u) du (c) f² ebx dxarrow_forward
- Find the following limits. (a) lim 3(x-1)² x→2 x (b) lim 0+x (c) lim 3x2-x+1 x²+3 x²+x-12 x-3 x-3arrow_forwardFor f(x) = (x+3)² - 2 sketch f(x), f(x), f(x − 2), and f(x) — 2. State the coordi- nates of the turning point in each graph.arrow_forwardFor f(x) = (x+3)² - 2 sketch f(x), f(x), f(x − 2), and f(x) — 2. State the coordi- nates of the turning point in each graph.arrow_forward
- 4 For the function f(x) = 4e¯x, find f''(x). Then find f''(0) and f''(1).arrow_forwardSolve the next ED: (see image)arrow_forwardWrite an equation for the polynomial graphed below. It will probably be easiest to leave your "a" value as a fraction. 8 7 + 9+ H 6 5 4 3 + 3 2 1 (-30) (-1,0) (1,0) (3,0) + -5 -4 -3 -2 2 3 4 7 2 -1 -2 3 (0,-3) f(x) = 456 -4 -5 -6+arrow_forward
- Calculus: Early TranscendentalsCalculusISBN:9781285741550Author:James StewartPublisher:Cengage LearningThomas' Calculus (14th Edition)CalculusISBN:9780134438986Author:Joel R. Hass, Christopher E. Heil, Maurice D. WeirPublisher:PEARSONCalculus: Early Transcendentals (3rd Edition)CalculusISBN:9780134763644Author:William L. Briggs, Lyle Cochran, Bernard Gillett, Eric SchulzPublisher:PEARSON
- Calculus: Early TranscendentalsCalculusISBN:9781319050740Author:Jon Rogawski, Colin Adams, Robert FranzosaPublisher:W. H. FreemanCalculus: Early Transcendental FunctionsCalculusISBN:9781337552516Author:Ron Larson, Bruce H. EdwardsPublisher:Cengage Learning





