question about matrix division (I'm getting division by 0?)

Linear spaces and subspaces, linear transformations, bases, etc.
lawrence
Posts: 15
Joined: Wed Apr 01, 2009 10:48 pm

question about matrix division (I'm getting division by 0?)

I have a question about matrix multiplication; well, actually, matrix division. I am assuming that matrices are divided the same as they are multiplied; that is, row by column. Specifically, the problem I am referring to:
[ 2  1 ] * A = [ 3  0 ]
[ 0  3 ]       [-3  6 ]
To solve for A, would you divide the right matrix by the one on the left? If so, I come up with the following:
[ 3/2       3 ]
[-3/2+6/0  -1 ]
But what do I do with that 6/0?

Martingale
Posts: 333
Joined: Mon Mar 30, 2009 1:30 pm
Location: USA
Contact:

Re: question about matrix division (I'm getting division by 0?)

I have a question about matrix multiplication; well, actually, matrix division. I am assuming that matrices are divided the same as they are multiplied; that is, row by column. Specifically, the problem I am referring to:
[ 2  1 ] * A = [ 3  0 ]
[ 0  3 ]       [-3  6 ]
To solve for A, would you divide the right matrix by the one on the left? If so, I come up with the following:
[ 3/2       3 ]
[-3/2+6/0  -1 ]
But what do I do with that 6/0?
you need to find the inverse matrix for $\left[\begin{array}{cc}2&1\\0&3\end{array}\right]$

and multiply that to both sides

stapel_eliz
Posts: 1628
Joined: Mon Dec 08, 2008 4:22 pm
Contact:
I have a question about matrix multiplication; well, actually, matrix division. I am assuming that matrices are divided the same as they are multiplied...
No; division is not defined for matrices. As the previous reply suggests, you have to use a different process. (I'm guessing you're self-studying or thinking ahead of your class syllabus...?)

With numbers, dividing by a value was the same as multiplying by the "multiplicative inverse", being the reciprocal of the intended divisor. For instance, 10 divided by 2 is the same as 10 times 1/2.

While matrices cannot be divided, they can (sometimes) have multiplicative inverses. To learn about this topic and the process for finding an inverse, try here.

lawrence
Posts: 15
Joined: Wed Apr 01, 2009 10:48 pm

Thank you both!