Help with Matricies

Numbah51 · #1 $Old$ October 26th, 2008, 12:58 PM

I have a problem in which i need to find a matrix A, such that

[1 3 2] [7 1 3]
[2 1 1] A = [1 0 3]
[4 0 3] [-1 -3 7]

I have no idea on how to go about figuring this out. I'd normally think Divide the one on the right by the one on the left, but that wouldn't work with matrices. Any help would be greatly appreciated.

Rafael Almeida · #2 $Old$ October 26th, 2008, 01:09 PM

If i understood well, you need to find the matrix X witch suffices

$AX = B$ , with

$A = \left(\begin{array}{ccc}1&3&2\\2&1&1\\4&0&3\end{array}\right) B = \left(\begin{array}{ccc}7&1&3\\1&0&3\\-1&-3&7\end{array}\right)$

Sure you can't really divide one matrix by another, as this is not defined.

Notice that my matrix X is your matrix A. You can find X by solving the system. To do so, you create the associated matrix of the system and put it into reduced by rows form.

If you're not supposed to know how to resolve linear systems escalonating matrices, you can assume $X = \left(\begin{array}{ccc}a&b&c\\d&e&f\\g&h&i\end{array}\right)$ , do the multiplication and then equal the matrices, term by term. Please notice that this is what you'll be doing with the row reduction process.

Edit:

I'm not going into the details of row-reducing right here, you should check your textbook for the algorithm. Mathematica yields me the row reduced associated matrix as being

$R = \left(\begin{array}{cccccc}1&0&0&-1&0&1\\0&1&0&2&1&0\\0&0&1&1&-&1\end{array}\right)$

And so, the matrix X (or A, in your post) that you are looking for is:

$\left(\begin{array}{ccc}-1&0&1\\2&1&0\\1&-1&1\end{array}\right)$

If you have a doubt in some part of the solution, feel free to post back,

Soroban · #3 $Old$ October 26th, 2008, 01:25 PM

Hello, Numbah51!

It looks like you missed a few lectures
. . or your professor didn't explain the required material.

Quote:

Find a matrix $A$ , such that: . $\begin{bmatrix} 1 & 3 & 2 \\ 2 & 1 & 1 \\ 4 & 0 & 3\end{bmatrix}\,A \;=\;\begin{bmatrix} 7 &1&3 \\ 1&0&3\\ \text{-}1&\text{-}3&7 \end{bmatrix}$

You're expected to know about Inverse Matrices and how to find them.

Find the inverse of $\begin{bmatrix}1&3&2\\2&1&1\\4&0&3\end{bmatrix}$ .and left-multiply both sides of the equation.

Numbah51 · #4 $Old$ October 26th, 2008, 01:57 PM

Thanks for your help guys, i think i got it. I also need help with Big-O, but i'll start a new thread for that.