Question

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.

Answer 1

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.

Raj got from the phrase to encoded matrix by:

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.

To find the secret phrase we will reverse the steps as:

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).

Answer 2

Answer:c

Step-by-step explanation: