3. In computer science, we often make use of encryption algorithms to keep our messages and data secure. One form of representing message encryption lies in using matrices and their corresponding inverses. We can convert each letter to a number (e.g. its order in alphabets) and then transform them by an encryption matrix. Suppose we start with some message represented by a string. Each character in this message is assigned a corresponding number to each of its letter in the alphabet and then partitioned into 2D vectors. We can pick an arbitrary 2 x 2 encoding matrix A that is invertible and multiply the matrix A with them to encode th For example, assume we want to encrypt the "GET HELP". It can be represented as an orde letters: 'G', 'E', 'T', ' ; 'H, 'E', 'L; 'P. The order of - letters in the alphabets are 7, 5, 20, 0, 8, 5, 12, 16, respectively. In this message 0 represent an empty space. We can pick an arbitrary 2 x 2 encoding matrix A that is invertible and transform every pair of numbers. Assume -1 our encoding matrix is A = We can partition our message to 2D vectors as and then multiply matrix A with each of these vectors. The result is . Therefore the encoded message becomes 9, 11, 40, 60, 11, 14, 8, 4. The inverse of matrix A is A- = [3 .We can decipher the original message from the encoded message by multiplying A- to the encoded message. a) Using the encoding matrix A = encode -2 the strings "MATRIX". b) Using the encoding matrix A = decode encoded messages: 22, 27, 3, 23, 15, 33. c) If we happen to have an encoded string along with its decoded message, can we discover the encoding matrix? If so, is there any restriction on the length of this message?

Q: 1 -3 4 1 Let A = 1 2 -3 2 4. B = -4 0 -2 [-1 2 5. Find Rank of AB

A:

Q: 2/18 – 12/32 + 3V50

A: The solution is given below in the next step:

Q: A curve is given by the equation y = ln (2³+¹). x5

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Q: #1 only

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Q: -7 5 1 9 0 -2 -1 2 -1 4

A:

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A: I = ∫4x e−3x dx

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A:

Q: 3s – 7 s- 2s + 3

A:

Q: 2 3 B={ A= 3 Find: A+B .B+A .A-

A:

Q: 1) S7 (1+x*)²

A: Given: I=∫x3dx1+x42 For evaluating given integral, we substitute 1+x4=t…

Q: - 3 4 3 - 13 - 10 - 10 -3 Find the LU factorization of 9 L = U = II

A:

Q: +–3m+–9m+4+5+–10m

A: The expression is given as 1+–3m+–9m+4+5+–10m. Simplifying the given expression. 1+–3m+–9m+4+5+–10m…

Q: 6 5 3 5 6 2 Let D =| 4 -5 7 and E = 1 0 7 1 0 -3 2 5 Find - 5D- 6E.

A: given matrices are

Q: 目 +8 LI +T 现 +04 +C4 |F|E|F|| ||||4 4 4 2 2

A:

Q: 0 1 2 4 0 2 4 0 0 3 9 12

A:

Q: 2(3+d-1)

A: Solve the given expression  given expression is 2(3+d-1)

Q: 1 3 -2 What is the rank of 2? -81 -1 -2 -6 4 a. 4 с. 2 b. 3 d. 1

A: Given: The matrix, 13-2401-12-2-64-8 To find: The rank of the matrix.

Q: 14. (27 – 3 + 3k ) + 3(7 – !J + k )

A:

Q: 1 + 2n < n° for all integers n² 2

A:

Q: Find A

A:

Q: 4.) Which expressions have a negative product? Select all that apply. A. (-1)(2)(-3) B. -(-3)(-2) C.…

A: Solve the following

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A: We have find givan normal distribution...

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A: Evaluate -3d6w33=?

Q: 1 3 8.

A:

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A:

Q: 5 (4k + 3) k 1

A: Given,

Q: Prove that n² +n is divisible by 2, where n E N.

A:

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A: Given:The indefinite integral given is

Q: A. 3- 2x 2 x B. (2 - x) 2 3x C. 3(2 - X) 2 3x D. 3-2x2 3x 32. Six is at least the product of three…

A:

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A: Obtain the velocity vector as shown below: vt→=ddtrt→vt→=ddtsint,t,costvt→=cost,1,-sint

Q: 2/5 +7/12

A: Please see the answer below.

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A: Here we have to divide two polynomials as shown.

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A:

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A: We need to solve algebraic quantity.

Q: 2. (1 + 3/2x − 1)² = 3 + √3/2x − 1

A:

Q: 3(m – 5) + m

A: 3(m-5)+m=0 3m-15+m=0 add both side 15 we get 2m=15

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A: To solve the following problem

Q: The expansion of 500P3 is

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Contingency Table

A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.

Binomial Distribution

Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.