Question

How do you multiply matrices `A =((1, 2, 1), (-1, -1, 2), (-1, 1, -2))` and `B=((1, -1), (0, -1), (-1, 1))`?

Answer 1

`"A X B" = ((" "0,-2),(-3, " "4),(" "1,-2))`

Explanation:

Before you can multiply matrices, you have to check that they are compatible, Matrices are named according to the number of rows (horizontal) and columns (vertical).

A is a `3 xx 3` matrix read as "3 by 3"
and B is a `3 xx 2` matrix - "3 by 2"

`A xx B` means `color(blue)(3) xx color(red)(3)` and `color(red)(3) xx color(blue)(2)`

This is only possible if the middle 2 numbers are the same
- in this case shown in `color(red)"red"`

The answer will be a `color(blue)(3 xx 2)` matrix - (the outer numbers)

Each ROW in A must be multiplied by each COLUMN in B.
This involves multiplying the elements in the row by the elements in B and adding them together to get a single answer.

`"A X B" = ((1, 2, 1), (-1, -1, 2), (-1, 1, -2)) ((1, -1), (0, -1), (-1, 1))`

`(1,2,1) " must be multiplied by "(1,0,-1)`
This gives: `1+0-1 = 0 " "larr` 1st row, 1st column .

`(-1,-1,2) " multiplied by " (1,0,-1)`
This gives `-1+0-2 = -3" "larr` 2nd row, 1st column

`(-1,1,-2) " multiplied by "(1,0,-1)`
This gives `-1+0+2 = 1" "larr` 3rd row, 1st column

`(1,2,1) " multiplied by " (-1,-1,1)`
This gives `-1-2+1 = -2" "larr`1st row 2nd column

`(-1,-1,2) " multiplied by " (-1,-1,1`
This gives `1+1+2 = 4" "larr` 2nd row 2nd column

`(-1,1,-2) " multiplied by " (-1,-1,1)`
This gives `1-1-2 = -2" "larr` 3rd row 2nd column

`"A X B" = ((" "0,-2),(-3, " "4),(" "1,-2))`