Question

How do you multiply the matrices `((2, 1), (3, 0), (7, 4))` with `((2, 4), (5, 6))`?

Answer 1

Multiply rows from the first matrix by columns from the second matrix to get the row-column entry for the product.

Explanation:

`AxxB=C`

`((2,1),(3,0),(7,4))xx((2,4),(5,6))`

Row 1 of A: `(2,1)` times Column 1 of B: `((2),(4))`
gives Row 1: Column 1 of C: `((2xx2+1xx5,"?"),("?","?"),("?","?"))`

Row 1 of A: `(2,1)` times Column 2 of B: `((4),(0))`
gives Row 1: Column 2 of C: `((2xx2+1xx5,2xx4+1xx0),("?","?"),("?","?"))`

Row 2 of A: `3,0)` times Column 1 of B: `((2),(4))`
gives Row 1: Column 1 of C: `((32xx2+1xx5,2xx4+1xx0),(3xx2+0xx5,"?"),("?","?"))`

Continue on in this fashion to get:
`((2xx2+1xx5,2xx4+1xx0),(3xx2+0xx5,3xx4+0xx),(7xx2+4xx5,7xx4+4xx0)) = ((9,8),(6,12),(34,28))`

As a memory aid think about looking at these problems:
through `color(red)("rose col"`ored glasses.
i.e. `color(red)("rows")` first then `color(red)("col")`umns.