Video:How to Divide Matrices

Transcript:How to Divide Matrices

Hi, my name is Bassem Saad. I'm a Math Ph.D. candidate at U.C. Davis, and I'm here today for About.com to show you how to divide matrices.

Find the Matrix's Inverse to Divide

When I say I want to divide one matrix into another matrix, I really mean I want to multiply one matrix by the inverse of another matrix. So before you're able to divide a matrix, you must be able to find the inverse of a matrix and multiply matrices. So let's go ahead and multiply this matrix times the inverse of this matrix. I'm going to go ahead and copy the left-most matrix right underneath – two, four, six, eight. And I'm going to go ahead and put the inverse of this matrix right below it – one half, one half, minus one half, and another one half.

Multiply the Matrices

Now, we can go ahead and just do regular matrix multiplication. So we have the first row times the first column to give us our first element. That would be one minus two, gives us minus one. Then we have the first row times the second column, which gives us one plus two, or three. Then the second row times the first column, which is three minus four, which is minus one. And finally, the second row times the second column, which is three plus four, which is seven.

Dividing matrices is a useful step in solving linear equations. Civil engineers use this skill to help design structures and you can always find applications in scientific research. Thanks for watching, and to learn more, visit us on the web at About.com.