Matrices are commonly used to encrypt data. Here is a simple form such an encryption can take. First, we represent each letter in the alphabet by a number, so let us take < space > = 0, A = 1, B = 2, and so on. Thus, for example, "ABORT MISSION" becomes[1  2  15  18  20  0  13  9  19  19  9  15  14].To encrypt this coded phrase, we use an invertible matrix of any size with integer entries. For instance, let us take A to be the 2 × 2 matrix  34 21. We can first arrange the coded sequence of numbers in the form of a matrix with two rows (using zero in the last place if we have an odd number of characters) and then multiply on the left by A.Encrypted Matrix =  34 21 115201319914 2180919150  =  1111760751338742 4484035573328,which we can also write as[11  4  117  48  60  40  75  35  133  57  87  33  42  28].To decipher the encoded message, multiply the encrypted matrix by A−1. The following question uses the above matrix A for encoding and decoding.Decode the following message, which was encrypted using the matrix A. (Include any appropriate spaces in your answer.)[69  21  126  54  27  13  60  40  59  16  149  61  87  28]

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Matrices are commonly used to encrypt data. Here is a simple form such an encryption can take. First, we represent each letter in the alphabet by a number, so let us take < space > = 0, A = 1, B = 2, and so on. Thus, for example, "ABORT MISSION" becomes

[1  2  15  18  20  0  13  9  19  19  9  15  14].

To encrypt this coded phrase, we use an invertible matrix of any size with integer entries. For instance, let us take A to be the 2 × 2 matrix

3 4
2 1
.

We can first arrange the coded sequence of numbers in the form of a matrix with two rows (using zero in the last place if we have an odd number of characters) and then multiply on the left by A.

Encrypted Matrix  =
3 4
2 1
1 15 20 13 19 9 14
2 18 0 9 19 15 0
=
11 117 60 75 133 87 42
4 48 40 35 57 33 28
,

which we can also write as

[11  4  117  48  60  40  75  35  133  57  87  33  42  28].

To decipher the encoded message, multiply the encrypted matrix by

A−1.

The following question uses the above matrix A for encoding and decoding.

Decode the following message, which was encrypted using the matrix A. (Include any appropriate spaces in your answer.)

[69  21  126  54  27  13  60  40  59  16  149  61  87  28]
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Step 1

Consider the given question,

Find the inverse of the matrix A,

Step 2

Multiply the Encrypted matrix wit...

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