Exercises: Use Matrices to Represent Data

A matrix has 3 rows and 5 columns. What are its dimensions?

In the notation $a_{ij}$, what does the subscript $i$ refer to?

A store tracks weekly sales of 4 products in 3 regions. Which matrix size best encodes this data with rows = products and columns = regions?

The matrix $A = \begin{bmatrix} 7 & 2 & 5 \\ 1 & 9 & 4 \end{bmatrix}$ — what are its dimensions?

A matrix $B$ is described as $4 \times 2$. How many columns does it have?

Let $A = \begin{bmatrix} 3 & 7 & 1 \\ 2 & 0 & 5 \\ 8 & 4 & 6 \end{bmatrix}$. What is $a_{23}$?

Let $A = \begin{bmatrix} 3 & 7 & 1 \\ 2 & 0 & 5 \\ 8 & 4 & 6 \end{bmatrix}$. What is $a_{31}$?