Subject: Linear Algebra Name: Hoda
Who is asking: Student Question: 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. But what happens if you have to divide by zero? How does this affect the resulting matrix? Specifically, the problem I am referring to: To solve for A, you divide the right matrix by the one on the left. I come up with the following: What do I do with that 6/0? Hi Hoda, Unfortunately the matrix "division" operation you defined doesn't work the way you want it to.
Compare your problem to a problem with numbers: The point of this very basic example is to illustrate the same technique for matrices. In matrix multiplication the identity matrix I palys the roll of 1 since, for any 2 by 2 matrix A, I x A = A.
Note that if we multiply
we get compare to (1/6) (6) = 1
Hence your system by premultiplying both sides by the above matrix. You
get: For more information on such matrix inverses, and how to find them (it looks like we "pulled it out of a hat") consult a Linear Algebra text.
Hope this gives you a start,
