Lesson 1 of 13 · 7 min

What a matrix is

NCERT §3.1–3.2

Monday's stationery order arrives as a scribbled note: 11A wants 30 pens and 12 exercise books, 11B wants 25 pens and 20 books, 11C wants 18 pens and 15 books. The clerk at the counter redraws it as a table.

The story this chapter follows: The stationery counter

A school's stationery counter takes orders from every class, keeps price lists and writes bills. Its tables of classes by items are matrices, and its bills are matrix products. This chapter learns to read, combine, multiply, turn over and undo those tables.

The lesson in notes

In short

A matrix is a rectangular array of numbers (or functions) arranged in rows and columns and written inside brackets. Each number in it is an entry, or element.

The position of an entry carries meaning. If rows are pupils and columns are items, the entry in row 2 and column 1 is the number of the first item held by the second pupil.

Matrices are named with capital letters: A, B, X. The horizontal lines of entries are rows; the vertical lines are columns.

The same data can be laid out either way round. A table of 3 people by 2 items becomes a matrix with 3 rows and 2 columns, or, turned over, one with 2 rows and 3 columns.

A point (x, y) can be written as a column matrix with entries x and y, or as the row [x y]. A polygon's vertices can be stacked into one matrix, one column (or row) per vertex.

Matrices grew out of the need to handle systems of linear equations compactly. They are used in spreadsheets, cryptography, computer graphics (rotation, reflection, magnification) and economics.

In this chapter every entry is a real number or a real-valued function.