Please show me how to do this matrix problem. Thanks.

R

rachaelmaria7

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Nov 20, 2005
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I am trying to help a friend with algebra homework and I am so confused as to how to do this problem. This is the problem, if someone can show me how to do it so I can show/help her I would appriciate it. Thanks.

Question reads.......

B= | 1 0 1 0 1 |
| 0 1 1 0 3 |
| 2 1 1 1 1 |
| 0 0 1 0 2 |
| 1 1 1 2 1 |

The following message was encoded with the matrix B given above. Decode this message.

22 15 57 5 47 54 58 89 45 84 46 80
87 53 96 51 68 116 39 113 68 135 136
81 149
 
Since we don't know what the "code" was or what the coding process was, I'm not sure how to explain how to undo the coding. Messages are usually written in alphabetical characters. Were letters switched for numbers in some manner? How was the matrix used?

Please reply with a full explanation of this exercise. A related example from the text would likely be very helpful. Thank you.

Eliz.
 
Hello, rachaelmaria7!

Since the message also has 25 numbers, I suspect it is also a \(\displaystyle 5\times5\) matrix.

\(\displaystyle B\;=\;\begin{vmatrix}1 & 0 & 1 & 0 & 1 \\ 0 & 1 & 1 & 0 & 3\\2 & 1 & 1 & 1 & 1\\ 0 & 0 & 1 & 0 & 2\\1 & 1 & 1 & 2 & 1 \end{vmatrix}\)

The following message was encoded with the matrix B given above.
Decode this message.

\(\displaystyle C\;=\;\begin{vmatrix}22 & 15 & 57 & 5 & 47\\ 54 & 58 & 89 & 45 & 84\\ 46 & 80 & 87 & 53 & 96 \\ 51 & 68 & 116 & 39 & 113 \\ 68 & 135 & 136 & 81 & 149\end{vmatrix}\)
Click to expand...
More suspicions:

I believe the message matrix, \(\displaystyle A\), was a \(\displaystyle 5\times5\) matrix with 25 numbers

. . probably with the code: \(\displaystyle 1=A,\,2=B,\,3=C,\cdots\)

I think the message was encrypted with: .\(\displaystyle B\cdot A\:=\:C\)

. . and we want \(\displaystyle A\).


Hence, we must find \(\displaystyle B^{-1}\)

. . then: .\(\displaystyle B^{-1}\cdot B\cdot A\;=\;B^{-1}\cdot C\;\;\Rightarrow\;\;A\;=\;B^{-1}\cdot C\)
 
Just follow Soroban's instructions: Multiply C by B<sup>-1</sup>.

Eliz.
 
Where are you stuck? Are you having trouble finding the inverse matrix, or multiplying the inverse by C?

Please reply with specifics. Thank you.

Eliz.

P.S. When you reply, please specify whether you are using a graphing calculator. Thank you.
 
I am trying to do this so I can match my answer up with a friend since this is her problem so she can know if she is doing it right and what she does wrong. I don't know how to do a matrix on my graphing calc. That is why I am trying t find the steps in doing this so I can help her further.
 
Since this is a "coding" problem, shouldn't we be able to check the answer by finding, I dunno, some sensible sentence?

What is the "coding" process? I mean, if Soroban is correct about the list of numbers actually being from a matrix, and the matrix being the matrix C he came up with, and the process having been multiplication so the "uncoding" process is inversion and multiplication, then what will the numbers we get after multiplication mean? How would these numbers translate into whatever the original uncoded message was?

(We can't see your friend's book, so we're just guessing here. You'll need to fill in the gaps, if we're to get much further with this.)

If you have a graphing calculator and your friend is doing matrices, she'll likely know how to enter matrices into the graphing calculator, and she'll easily figure out (if she doesn't already know) how to do matrix inversion and multiplication. That will give her the correct form of A (modulo some round-off error; she may have to just "know" that entries like "-0.000000000005" are actually "0" or "4.9999999999" are actually "5").

Then follow whatever coding-uncoding process the book gave to find the original message. If you get something intelligible ("matrices are really cool", "the dog barked at midnight", etc), then you can be fairly certain that you did it right.

Eliz.
 
Well, where are you having trouble? If you're having trouble with inverting the matrix, please reply showing how far you've gotten, and I'll be glad to verify or correct what you've done. If you've already gotten the inverse and are having trouble getting the same answer she did upon multiplication, please reply with what you and she have gotten, and I'll be glad to correct or confirm.

Thank you.

Eliz.
 
Stapel just needs you to show your work but from what I am gathering you don't knwo what you are doing, just trying to help a friend. I can try toput some stepstogether but I am terrible when it comes to matrix. Can someone else show her so she can help her friend.
 
code1kd.gif

It does not look very promising does it?
The matrix B does have a rather nice inverse.
So that part is most likely correct.
I do question matrix C.
Is there more to the problem than has been posted.
 
Yeah PKA! So is that how the answer should look? I posted everything that was in her book. I am so confused on this martix stuff. I havent taken algebra in a few years but I was good at it so who does she come to when she needs some help? ME! UGH! :cry: Me being the good friend I am at work trying to help her with this. nto getting to far so I came on here for help so I can show her the steps tonight and see if she did it right.
 
You asked, “So is that how the answer should look?”
Well to be honest: I HAVE NO IDEA.
The encoding could have been A*B=C in which case A=C*B<SUP>−1</SUP>.
But you did not say if the interpretation of matrix C is correct!
 
Ok, well I am just trying to help her get the right answer, but I am not sure if that is going to happen because I am confused now myself!
 
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