Determinants
Work out 2 × 2 and 3 × 3 determinants, see what swapping rows does, and see how the determinant scales areas.
- UK: Year 12
- Iran: grade 12
- Afghanistan: grade 11
- Syria: grade 10
- Palestine: grade 11
- Russia: grade 10
Guide
The determinant is a number that belongs to a square matrix. For order 2 it is ad − bc: the product on the main diagonal minus the product on the other diagonal.
For order 3 expand along a row: each entry times the determinant of what is left when its row and column are crossed out. The signs go + − + along the row. Forgetting the alternating signs is the common slip.
Swapping two rows changes the sign of the determinant. A matrix as a transformation multiplies every area by the absolute value of its determinant.
Bars (vertical lines) mean the determinant, brackets mean the matrix. Ask your child why it is a number, not a table.