Problems
Cryptography. The following message was encoded with matrix A. Decode this message:
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- Start with the following matrix: 8-78 -9-10 9 -8 -3 -7 Perform the following 3 elementary row operations, one after the other, and give the resulting matrix at each step: You can resize a matrix (when appropriate) by clicking and dragging the bottom-right corner of the matrix. a) Add-2 times row 1 to row 2 000 000 000 b) Multiply row 3 by 5 000 000 000 1 c) Interchange rows 1 and 2 000 000 000arrow_forwarda. Use the coding matrix A = b. Use its inverse, A¹ 0 3 5 3 5 5 0 to encode the word WIPE. to decode 15, 55, 54, 59.arrow_forward1. Given the matrix A 1357. What is the inverse of A? A. -187-3-51 B. 187-3-51 C. -167-3-51 D. 167-3-51arrow_forward
- 2 31 to decode the cryptogram: 4. Use the inverse of the matrix A = 51 72 27 38 27 36 38 57 59 81 42 61 Enter the statement obtained in the space provided. HINT multiplly each coded row matrix on the right. Show ALL Workings Paragrapharrow_forward3. Add the matrices: 11 4 -1 0 1 -1 2 4 5 6 3 4 0 -4 3 6 3 -7 5 1 -1 0 6 7 3 5 --5 2arrow_forwardBlank A B C D E F G H I J K L M N O P Q R S T U V W X Y Z 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 0 1 2 3 4 5 6 7 [²32] 1. Using the cryptography code above, the following message was encoded with matrix A. Decode this message, to reveal the title of a movie, which is a favorite of one of your classmates. 26 27 56 69 78 97 12 12 28 29 72 87 38 57 Suppose matrix A = Suppose matrix C - 2 2 2 2 3 2 2 2 3 2. Using the same code, the following message was encoded with matrix C. Decode the message, to reveal the title of a book, that is a favorite of one of your classmates. 70 85 70 64 73 76 26 26 27 56 69 71 46 57 55 46 53 48 62 80 66arrow_forward
- 3. Let A be a 2 x 3 matrix, B a 3 × 4 matrix, and C a 4 x 5 matrix. The triple product ABC can be computed in two different ways: as (AB)C or as A(BC). (The fact that these always give the same answer is known as the associative law, Theorem 2(a) in section 2.1 of the textbook.) How many pairs of real numbers must be multiplied in the process of computing (AB)C? What about A(BC)? Which way of computing ABC is more efficient? To make sure you're on the right track in Problem 3, it takes eight multiplications to compute the product of two 2 x 2 matrices in the usual way. (If you're interested, you can read online about Strassen's algorithm which multiplies two 2x2 matrices in a more complicated way that uses only seven multiplications. Problem 3, however, asks only about “traditional" matrix multiplication using the row-column rule.)arrow_forward3. Select all the correct answers. If matrix D is a 7 x 4 matrix, and the product of matrix D and matrix E, DE, exists, what could be the order of matrix E? ロ7×4 4 x 4 ロ7x7 4 x 7 04x5 ロ7×5 Reset Next tuR All rights reservedarrow_forwardCompute the following matrix. -2 -1 -3 -1 -1 -4 -3 -3 3 -1 + 1 2 3 4 5 6 =arrow_forward
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