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: 45x(4²)3 3. Express as a single power. 48 a. 43 b. 42 C. 418 d. 46

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Q: 10 14 9.) Find O 18

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Q: -3 1 8 3 7 -1 4 0 5 3]

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Q: 2(-ャ) n=2

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Q: Expand (x + y) 8.

A: Given: The expression x+y8.

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: 1. In circle A below, which of the following is not true? O EF is a chord CB is a tangent line BA is…

A:

Q: A 2/15 B 30 V35 5 20

A: Given,  A circle with secant and tangent  We have to find the value of x

Q: 2. 2. 2. t.

A: Solution: The given equation is 2∂2u∂x2=∂2u∂t2+2x Rewrite it ∂2u∂t2-22∂2u∂x2=2x Conditions ux0,t=et…

Q: d. 1 3a+18 = 1 - 8 a+6

A:

Q: 5 L s² + 2s – 3

A: We know that, Laplace transform of 1/(s-1) = e^t

Q: (カナ) 2.

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Q: 1) (8s° - 9s) - (3s° + 4)

A: Since you have asked multiple question, we will solve the first question for you. If youwant any…

Q: 1. Plot each of the following polar coordinates:

A: Given, To plot (5,5π3) and (2,-5π4)

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A: We have to find that the gas is enough or not to reach at point C.

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A: We have to find Laplace inverse by convolution theorem.

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A: I have to exapand (5a^2-2b)

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Q: find: (m+I) m!

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A: 16-3275-834-634perform -2R1+R2

Q: Find A.

A: Given

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A:

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Q: - [B 3. A = 935 14 -2

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: We have to find the given triple integral

Q: 6 1/6 + 6

A:

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.