# Homework Help: Matrix multiplication

1. Sep 2, 2008

### Shaun Culver

1. The problem statement, all variables and given/known data

Prove the formula.

2. Relevant equations

Matrix multiplication:
$$(\text{AB})_{i \,j}=\sum _{k=1}^n a_{i \,k}b_{k \,j}$$

3. The attempt at a solution

I do not know how to "prove" the formula for arbitrary values of $k$ and $n$.

2. Sep 2, 2008

3. Sep 2, 2008

4. Sep 2, 2008

### HallsofIvy

Okay, what he is doing is defining the matrix corresponding to a linear transformation, then defining the multiplication of two matrices as the matrix corresponding to the composition of the two corresponding linear transformation, finally giving that formula. What is asked here is that you show that this formula really does give the matrix corresponding to the composition of two linear transformations. I would recommend that you look at what the linear transformations and the two matrices do to each of the basis vectors in turn.

Share this great discussion with others via Reddit, Google+, Twitter, or Facebook