A matrix is a table you can do arithmetic with
Adding two matrices is easy: add the numbers that sit in the same place. The two matrices have to be the same size, because a number with nothing to pair up with cannot be added.
| 2 | 5 |
| 1 | 0 |
Class 12 · 16 games
Matrix algebra, explained with pictures
A block of numbers you can add and multiply as one object.
In everyday life: A timetable, a price list for three shops, the scores of four teams across five matches — any table of numbers you want to work with all at once.
Multiplying is row against column
To find the entry in row 1, column 2 of A x B, run along row 1 of A and down column 2 of B, multiply the pairs as you go, and add them up. It is not "multiply the numbers in the same place" — that is the one thing to unlearn.
| 1 | 2 |
| 0 | 3 |
| 4 | 1 |
| 2 | 5 |
The determinant is one number that describes the whole matrix
For a square matrix there is a single number, the determinant, that tells you whether the matrix can be undone. When it is zero, information has been lost and there is no way back.
| 3 | 1 |
| 2 | 4 |
A worked example
Work out the entry in row 1, column 1 of A x B, where the first row of A is (1, 2) and the first column of B is (4, 2).
| 1 | 2 |
| 0 | 3 |
| 4 | 1 |
| 2 | 5 |
8
Run along the row and down the column together: 1 x 4 is 4, and 2 x 2 is 4. Add them and you get 8. Every entry of the product is built this way.
Words to know
- entry
- One number inside the matrix, named by its row and its column.
- order
- The size of a matrix: rows first, then columns. A 2 x 3 matrix has 2 rows and 3 columns.
- determinant
- A single number worked out from a square matrix.
- minor
- The determinant of what is left after you cross out one row and one column.
In the games
You will fill in the entries of sums and products yourself, and expand a determinant one minor at a time.
Skills
- Add and multiply matrices · Class 12
- Determinant of a 3 x 3 matrix · Class 12
By class
Practise matrix algebra in Tivumo
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