## sloppycanada one year ago Rules of matrices I don't understand this multiply matrices thing, what is required for me to be able to do this?

1. anonymous

for the multiplication to be "legal"?

Yeah I guess? Particularly for uneven matrices like say A = 5x4 and B = 4x3 That sort of thing.

3. anonymous

stolen from wikipedia but the product AB is defined only if the number of columns in A is equal to the number of rows in B

4. anonymous

for example if A was 3x2 and B was 2x3 it'd be defined if A was 3x3 and B was 2x2 it wouldn't be defined

So 5x4 and 4x3 wouldn't work?

6. anonymous

look at the inner most numbers the way matrices are expressed it's rowx col

7. anonymous

so $$axb * cxd$$ is defined when b=c

8. anonymous

this is part of why matrix multiplication also isn't commutative for example, 2x2 * 1x2 isn't defined but 2x1 * 2x2 is defined

9. anonymous

and the outer numbers tells you the size of the product matrix. So a 2x1 * 2x2 multiplication will result in a 2x2 matrix and 5x4 * 4x3 gives a 5x3 matrix

10. anonymous

The number of columns of the left matrix must equal the rows of the right matrix.

11. anonymous

Matrices come from systems of equations. For example: $ax+by = e\\ cx+dy=f$We can write this a vector equation: $\begin{bmatrix}a\\c\end{bmatrix}x+\begin{bmatrix}b\\d\end{bmatrix}y=\begin{bmatrix}e\\f\end{bmatrix}$However, if we want to treat the variables $$x$$ and $$y$$ as components of a vector, then we need matrix multiplication to be defined to work this way:$\begin{bmatrix}a&b\\c&d\end{bmatrix}\begin{bmatrix}x\\y\end{bmatrix} = \begin{bmatrix}ax+by\\cx+dy\end{bmatrix}$This way we can say: $\begin{bmatrix}a&b\\c&d\end{bmatrix}\begin{bmatrix}x\\y\end{bmatrix} = \begin{bmatrix}e\\f \end{bmatrix}$

Okay... but 5x4 and 4x3 will work.

13. anonymous

Matrices are denoted with rows by columns. If the left matrix has 4 columns, and the right matrix has 4 rows, then it should work.

And we have 4 columns and 4 rows.