Question

The message 29 34 39 57 45 65 2 3 17 22 54 74 26 39 29 43 was encoded with matrix A. Decode the message.

A = [1 2, 1 3]
The message is:________.

Answer 1

The message is S E C R E T A G E N T M A N

Explanation:

This is a very easy exercise, follow the steps taken below:

Step 1: Find
`A^(-1)`

`A = \left[\begin{array}{ccc}1&2\\1&3\end{array}\right]`

Note that If
`M = \left[\begin{array}{ccc}a&b\\c&d\end{array}\right]`

then
`M^(-1) = \left[\begin{array}{ccc}a&-b\\-c&a\end{array}\right]`

Therefore,
`A^(-1) = \left[\begin{array}{ccc}3&-2\\-1&1\end{array}\right]`

Step 2: Find A⁻¹B ( i.e product of A and B)

`B = \left[\begin{array}{cccccccc}29&39&45&2&17&54&26&29\\34&57&65&3&22&74&39&43\end{array}\right]`

`A^(-1)B = \left[\begin{array}{cccccccc}19&3&5&0&7&14&0&1\\5&18&20&1&5&20&13&14\end{array}\right]`

Step 3: Decode the message in the matrix above

The message will be decoded in this order:

Note that 0 stands for empty space

19 5 3 18 5 20 0 1 7 5 14 20 0 13 1 14

S E C R E T A G E N T M A N

The message encoded is: S E C R E T A G E N T M A N