Question

Question #dd485

Answer 1

See below.

Explanation:

`A=((4,5,-2),(3,-1,0),(4,2,7))`

`B=((2,1,-1),(0,1,3),(5,7,3))`

Each element in B is multiplied by 2

`2B=2((2,1,-1),(0,1,3),(5,7,3))=((4,2,-2),(0,2,6),(10,14,6))`

Each element of A is added to the corresponding element of 2B

#A+2B=((4,5,-2),(3,-1,0),(4,2,7))+((4,2,-2),(0,2,6),(10,14,6)) =((8,7,-4),(3,1,6),(14,16,13))#

`(A+2B)B=((8,7,-4),(3,1,6),(14,16,13))((2,1,-1),(0,1,3),(5,7,3))= ((-4,-13,1),(36,46,18),(93,121,73))`

Each element in a row of A multiplies each element in the corresponding column of B, and these are added together to form each element of the product matrix.

Example using a `1xx1` and a `3xx1` matrix.

`((4,5,6))xx((1),(2),(3))=((4xx1)+(5xx2)+(6xx3))=(32)`

So we have 1st row x 1st column is 1st element in 1st row, 1st column. 2nd row x 1st column is 1st element in 2nd row, 1st column, and so on. This takes a bit of time to get confident with.

Note:

It is important to remember when multiplying matrices, that the order in which they are multiplied affects the product. In general for matrices A and B:

`AB != BA`