Practice Matrix Definition in Math
Use these practice problems to test your method after reviewing the concept explanation and worked examples.
Quick Recap
A matrix is a rectangular array of numbers arranged in rows (horizontal) and columns (vertical). An m \times n matrix has m rows and n columns. Each number in the matrix is called an entry or element, identified by its row and column position.
Think of a spreadsheet: rows go across, columns go down, and every cell holds a number. A 2 \times 3 matrix is like a mini-spreadsheet with 2 rows and 3 columns. Matrices package multiple numbers into a single organized object so you can manipulate them all at once.
Example 1
easyGiven A = \begin{bmatrix} 3 & -1 & 7 \\ 0 & 5 & 2 \end{bmatrix}, what are the dimensions of A and what is a_{2,3}?
Example 2
mediumWrite a 3 \times 1 column matrix where a_{i,1} = 2i - 1.
Example 3
easyWhat are the dimensions of \begin{bmatrix} 4 & 0 \\ -1 & 7 \\ 3 & 2 \end{bmatrix}?
Example 4
mediumIf A is a 4 \times 3 matrix, how many entries does it have? Can you multiply A by a 3 \times 5 matrix?