Question

Give the following four matrices, answer both questions:

A=⎡⎣⎢230⎤⎦⎥
, B=[3120]
, C=[123]
, D=⎡⎣⎢⎢⎢4321⎤⎦⎥⎥⎥

1. Choose two matrices to multiply together. What is the resulting matrix?

2. Choose two matrices that you CANNOT multiply together. Why can't you multiply them?

Answer 1

First note the sizes (as given):

- A = [2; 3; 0] is 3×1
- B = [3 1 2 0] is 1×4
- C = [1 2 3] is 1×3
- D = [4; 3; 2; 1] is 4×1

1) Example multiply: A·B is valid because A is 3×1 and B is 1×4, so the product is 3×4.
A·B =
[2; 3; 0] · [3 1 2 0] =
[[6 2 4 0],
[9 3 6 0],
[0 0 0 0]]

2) Example not allowed: C·D is not defined. C is 1×3 while D is 4×1; the inner dimensions (3 and 4) are not equal, so you cannot multiply C·D. (Likewise B·A is not allowed because 4 ≠ 3.)