Question

If `A=[(2,-1),(3,0),(1,2)]` and `B=[(3,2),(1,1)]`, find `2AB`?

Answer 1

`2AB=[(10,6),(18,12),(10,8)]`

Explanation:

As `A=[(2,-1),(3,0),(1,2)]` and `B=[(3,2),(1,1)]`

observe as `A` is a `3xx2` matrix and `B` is `2xx2` matrix,

we can multiply them as columns of `A` and rows of `B` are same and result will be a `3xx2` matrix.

In multiplication we multiply elements of `h^(th)` row of `A` with elements of `k^(th)` column of `B` to get the element of `k^(th)` column of `h^(th)` row.

Thus `2AB=2[(2xx3+(-1)xx1,2xx2+(-1)xx1),(3xx3+0xx1,3xx2+0xx1),(1xx3+2xx1,1xx2+2xx1)]`

= `2[(5,3),(9,6),(5,4)]=[(10,6),(18,12),(10,8)]`