Question

How do you multiply `((2, -3), (5, 1))` by `((1, -3, 4), (2, 4, 3))`?

Answer 1

`((2, -3), (5, 1)) xx ((1, -3, 4), (2, 4, 3)) = ((-4, -18, -1), (7, -11, 23))`

Explanation:

Check that the matrices are compatible.
Look at the format of each matrix - the Rows (R) and the Columns
(C)
R x C

The two 'middle' numbers must be the `color(red)"same"`
`color(blue)(2)xxcolor(red)(2) and color(red)(2)xxcolor(blue)(3)`

These are compatible. The answer will be a `color(blue)(2xx3)` matrix. `((R_1C_1, R_1C_2, R_1C_3), (R_2C_1, R_2C_2, R_2C_3))`

Each row in matrix 1 must be multiplied by each column in matrix 2.
The elements are all multiplied and then added together.

`((2, -3), (5, 1))` by `((1, -3, 4), (2, 4, 3)) = ((-4, -18, -1), (7, -11, 23))`

`R_1C_1 = 2-6 = -4`
`R_1C_2 = -6-12 = -18`
`R_1C_3 = 8-9 = -1`
`R_2C_1 = 5+2=7`
`R_2C_2 = -15+4 = -11`
`R_2C_3 = 20+3 = 23`