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

Answer:

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

Step-by-step 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)

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

$A^{-1} B = \left[\begin{array}{ccc}3&-2\\-1&1\end{array}\right] \left[\begin{array}{cccccccc}29&39&45&2&17&54&26&29\\34&57&65&3&22&74&39&43\end{array}\right]$

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

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