# Matrix division/inverse problem

• Oct 21st 2010, 11:16 PM
Jishent
Matrix division/inverse problem
Edmonton’s mayor is getting nervous about the upcoming municipal elections and wants to send a private message to his counsellors. One of his interns is taking linear algebra and helps him set up a matrix 𝑀 where each letter in the message is replaced by the number of its position in the alphabet. Thus, for example, “ESPIONAGE” becomes the matrix M=[5 19 16, 9 15 14, 1 7 5] (its a 3 x 3 matrix each comma representing a different row.

In order to avoid detection each message sent to counsellors is encoded as MK,
where K=[1 -3 0, -2 5 1, 0 1 0] ( 3x3 matrix as well) If the counsellors receive the matrix x [-8 29 15, -7 30 6, -8 16 13] what is the mayor trying to tell them?

so I did this:
MK=X
M(k^-1)k=(k^-1)x
M=(k^-1)x

Found the inverse of K so thats K^-1 and times it towards matrix X. I get negative numbers in the final matrix and numbers above 26 so i can't figure out the "code."

The K inverse is [1 0 3, 0 0 1, 2 1 1] what did I do wrong?
• Oct 21st 2010, 11:45 PM
Prove It
That's because if your equation is

$MK = X$

then

$MKK^{-1} = XK^{-1}$

$MI = XK^{-1}$

$M = XK^{-1}$.

You should have postmultiplied by the inverse of $K$.
• Oct 21st 2010, 11:52 PM
Jishent
Could you explain what you meant by "Postmultiplied by the inverse of K"?
• Oct 22nd 2010, 12:00 AM
Prove It
$XA$ is premultiplying by $X$ because the $X$ goes in front.

$AX$ is postmultiplying by $X$ because the $X$ goes behind.
• Oct 22nd 2010, 12:03 AM
Jishent
Wow....Thanks!