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djverab [1.8K]
3 years ago
9

Raj encoded a secret phrase using matrix multiplication. Using A = 1, B = 2, C = 3, and so on, he multiplied the clear text code

for each letter by the matrix to get a matrix that represents the encoded text. The matrix representing the encoded text is . What is the secret phrase? Determine the location of spaces after you decode the text.

Mathematics
2 answers:
pychu [463]3 years ago
7 0

Answer:c

Step-by-step explanation:

Natali5045456 [20]3 years ago
4 0

Answer:

THE CORN IS YUMMY

Step-by-step explanation:

Understanding the question:

Raj encoded a secret phrase using matrix multiplication. For that he first converted each letter in that phrase to integers using the following codes:

A=1,B=2,C=3,D=4,E=5,F=6,G=7,H=8,I=9,J=10,K=11,L=12,M=13,N=14,O=15,P=16,Q=17,R=18,S=19,T=20,U=21,V=22,W=23,X=24,Y=25,Z=26

We suppose that Raj had a matrix X formed by letters of that phrase encoded in integers/numbers. And he multiplied that matrix X with matrix C to get an encoded matrix, let us say 'encoded X'.

Where; C = \left[\begin{array}{ccc}2&5\\1&2\end{array}\right]

and encoded X = \left[\begin{array}{ccc}85&111&135&111&95&101&153\\38&48&55&45&41&44&64\end{array}\right]

What we need now is X.

<u>Raj got from the phrase to encoded matrix by:</u>

1. Encoding each letter into numbers and forming a matrix X.

2. Multiplying that matrix with another Matrix C to obtain the given encoded matrix.

<u>To find the secret phrase we will reverse the steps as:</u>

1. Multiplying the encoded matrix by 'Inverse of Matrix C' to get matrix X.

2. Converting the elements of X into alphabets.

Inverse of C = (Adjoint of C)/Determinant(C)

Adjoint of \left[\begin{array}{ccc}2&5\\1&2\end{array}\right] = \left[\begin{array}{ccc}2&-5\\-1&2\end{array}\right]

Determinant of C = |C| = ad - bc = 2*2 - 5*1 = -1

Inverse of C = \left[\begin{array}{ccc}2&-5\\-1&2\end{array}\right] / (-1)

= \left[\begin{array}{ccc}-2&5\\1&-2\end{array}\right]

Multiplying Inverse(C) and encoded X = \left[\begin{array}{ccc}-2&5\\1&-2\end{array}\right] \left[\begin{array}{ccc}85&111&135&111&95&101&153\\38&48&55&45&41&44&64\end{array}\right]

=\left[\begin{array}{ccc}20&8&5&3&15&18&14\\9&19&25&21&13&13&25\end{array}\right]

Converting these elements back to alphabets, we get:

=\left[\begin{array}{ccc}T&H&E&C&O&R&N\\I&S&Y&U&M&M&Y\end{array}\right]

Hence, it is obvious that the secret phrase is "THECORNISYUMMY"

The location of spaces are between every word ( THE CORN IS YUMMY).

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