please help me figure out how to decode this problem. i found the inverse but am unsure where to go from there as the numer of columns in the first matrix does not equal the number of rows in the second matrix so I can't multiply them together
please help me figure out how to decode this problem. i found the inverse but am unsure where to go from there as the numer of columns in the first matrix does not equal the number of rows in the second matrix so I can't multiply them together
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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please help me figure out how to decode this problem. i found the inverse but am unsure where to go from there as the numer of columns in the first matrix does not equal the number of rows in the second matrix so I can't multiply them together
![### Decoding an Encoded Message Using Matrix Operations
The following message was encoded using the 4x4 encoding matrix \( B \):
\[ B = \begin{bmatrix}
2 & 2 & 1 & 3 \\
1 & 1 & 0 & 1 \\
1 & 2 & 2 & 1 \\
2 & 3 & 2 & 3
\end{bmatrix} \]
The encoded message is:
```
85 27 74 109 31 13 27 40 106 47 62 121
56 14 55 77 75 28 74 107 28 14 25 39
```
To decode the encoded message, you are required to use the multiplicative inverse of the encoding matrix, \( B^{-1} \). Below are the steps you need to follow:
1. **Compute the Inverse of \( B \)**
2. **Post your matrix \( B^{-1} \)**
These steps involve the fundamental principles of linear algebra, specifically techniques for finding the inverse of a matrix, which can then be applied to the encoded message to retrieve the original data.
To further assist, here's a simplified outline of the decoding process:
1. **Compute the Inverse of \( B \)**: Use appropriate matrix inversion techniques, referencing any linear algebra textbook or resource, to find the inverse \( B^{-1} \).
2. **Apply \( B^{-1} \) to the Encoded Message**:
- Formulate the encoded message into matrices suitable for multiplication.
- Multiply each part of the encoded message by \( B^{-1} \) to extract the original message.
Please carry out the matrix computations accurately to ensure the correct original message is retrieved.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc0c29b48-6896-4921-8e61-0c75678e4051%2F8e3a06ac-b0d9-446e-be03-c25801f792ee%2Fponam5_processed.png&w=3840&q=75)
Transcribed Image Text:### Decoding an Encoded Message Using Matrix Operations
The following message was encoded using the 4x4 encoding matrix \( B \):
\[ B = \begin{bmatrix}
2 & 2 & 1 & 3 \\
1 & 1 & 0 & 1 \\
1 & 2 & 2 & 1 \\
2 & 3 & 2 & 3
\end{bmatrix} \]
The encoded message is:
```
85 27 74 109 31 13 27 40 106 47 62 121
56 14 55 77 75 28 74 107 28 14 25 39
```
To decode the encoded message, you are required to use the multiplicative inverse of the encoding matrix, \( B^{-1} \). Below are the steps you need to follow:
1. **Compute the Inverse of \( B \)**
2. **Post your matrix \( B^{-1} \)**
These steps involve the fundamental principles of linear algebra, specifically techniques for finding the inverse of a matrix, which can then be applied to the encoded message to retrieve the original data.
To further assist, here's a simplified outline of the decoding process:
1. **Compute the Inverse of \( B \)**: Use appropriate matrix inversion techniques, referencing any linear algebra textbook or resource, to find the inverse \( B^{-1} \).
2. **Apply \( B^{-1} \) to the Encoded Message**:
- Formulate the encoded message into matrices suitable for multiplication.
- Multiply each part of the encoded message by \( B^{-1} \) to extract the original message.
Please carry out the matrix computations accurately to ensure the correct original message is retrieved.
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