2 Matrix Multiplication

Matrix multiplication is performed by the operator %*%; for example, execute the command A%*%B. However, this will only work if the two matrices have matching dimensions. The dim command calculates the dimensions of a matrix, where the first number indicates the number of rows and the second indicates the number of columns:

dim( A )

dim( B )

dim( C )

dim( D )

dim( E )

Here, we see that matrix $C$ and matrix $D$ have a matching dimension and so we can execute the following matrix multiplication:

F <- C%*%D

F

dim( F )

When the dimensions of the matrices do not match, for example B%*%C, RStudio reports the message Error in B%*%C: non-conformable arguments.

 

Quiz 1: Matrix multiplication

For $𝐀,𝐁,𝐂,𝐃$ and $𝐄$ as defined by A,B,C,D and E at the start of this worksheet, find

${\mathrm{𝐂𝐀𝐁}}^T𝐃+\mathrm{𝐄𝐂𝐃}$

The result is

1. (A)

2. (B)

3. (C)

4. (D)

5. (E)