Definition: A matrix is a rectangular array of numbers arranged in rows and columns, used to organize data and to represent systems of equations and transformations.
What is a matrix?
A matrix is a grid of entries. Its dimensions are written rows by columns, so a matrix with 2 rows and 3 columns is a 2 by 3 matrix. The entry in row i, column j is called aij.
What can you do with matrices?
- Add or subtract matrices that have the same dimensions, entry by entry.
- Multiply by a scalar, which multiplies every entry.
- Multiply two matrices when the inner dimensions match.
Worked example: let A have rows (2, -1) and (4, 3). Then 3A has rows (6, -3) and (12, 9), and the entry a21 equals 4.
A bakery might store the number of loaves sold on three days in rows, one row per bread type; adding two weeks of data then means adding two matrices.
What do students confuse?
Reversing the order of rows and columns. A 2 by 3 matrix is not 3 by 2. Mathbot remembers it as “Roman Catholic”: rows first, columns second.
Example: A = [[2, -1], [4, 3]] is 2 by 2 with a21 = 4