2. Demonstrate how to use Excel to encrypt or code a message using matrices and their inverse. The message to be encoded is SEPTEBMER IS HERE The encoded message to be formed using triplets of numbers and the 3x3 matrix $\begin{pmatrix} 1 & 0 & 0 \\ 3 & 1 & 5 \\ -2 & 0 & 1 \end{pmatrix}$ whose inverse is $A^{-1} = \begin{pmatrix} 1 & 0 & 0 \\ -13 & 1 & -5 \\ 2 & 0 & 1 \end{pmatrix}$ Use the following association of letters and divide the message into triplets of letters: SEP TEM BER ISH ERE ABCDEFGHI J K L M N O P Q R S T U V W X Y Z 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 Now multiply the matrix A times each column vector of the message. You will receive the coded message. To decode the message, form 3x1 column vectors of the numbers in the coded message and multiply on the left by $A^{-1}$. Demonstrate how to use Excel to add and multiply matrices to prove the following properties of
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SEPTEMBER IS HERE can be represented as: S E P T E M B E R I S H E R E 19 4 15 20 4 12 1 4 17 8 19 7 4 17 4 Show more…
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Q1. A message is converted into numeric form by letting A = 1, B = 2, C = 3, ..., Y = 25 and Z = 26 or 0. Obtain the following Hill 2 cipher of the plain text "ATTEMPT" by using the key matrix [4 1] [5 5] Also decipher the text.
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One method of encryption is to use a matrix to encrypt the message and then use the corresponding inverse matrix to decode the message. The encrypted matrix, $E,$ is obtained by multiplying the message matrix, $M$ by a key matrix, $K .$ The original message can be retrieved by multiplying the encrypted matrix by the inverse of the key matrix. That is, $E=M \cdot K$ and $M=E \cdot K^{-1}$ (a) Given the key matrix $K=\left[\begin{array}{ccc}{2} & {1} & {1} \\ {1} & {1} & {0} \\ {1} & {1} & {1}\end{array}\right],$ find its inverse, $K^{-1} .$ [Note: This key matrix is known as the $Q_{2}^{3}$ Fibonacci encryption matrix. (b) Use your result from part (a) to decode the encrypted matrix $E=\left[\begin{array}{lll}{47} & {34} & {33} \\ {44} & {36} & {27} \\ {47} & {41} & {20}\end{array}\right]$ (c) Each entry in your result for part (b) represents the position of a letter in the English alphabet $(A=1, B=2$, $C=3, \text { and so on }) .$ What is the original message?
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The following message was encoded using the 4x4 encoding matrix B = Decode this message: To decode the encoded message, it requires using the multiplicative inverse of the encoding matrix, B. Use technology to compute the inverse of B. B^-1 (Type an integer or simplified fraction for each matrix element): Decode the message. Choose the correct answer below. RAWHIDE TO WALTER REED SKYLARK TO LEATHERNECK RAWHIDE TO LEATHERNECK SKYLARK TO WALTER REED
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