Matrices
Determinant
A number ad − bc found from a 2×2 matrix; if it is zero, the matrix has no inverse.
| English | Determinant |
|---|---|
| Bahasa Melayu | Penentu |
| 中文 | 行列式 |
How it is used
For M = (4 3; 2 5), the determinant is ad − bc = (4)(5) − (3)(2) = 20 − 6 = 14. Since 14 is not zero, M has an inverse.
Where it shows up in SPM
In the Matrices chapter (Form 5), always as a step before finding an inverse. In Paper 1 you compute a determinant quickly; in Paper 2 it is the first line of solving simultaneous linear equations by the matrix method.
Don't confuse it with
Frequently asked questions
What does it mean when the determinant is zero?
A zero determinant means the matrix has no inverse, so you cannot use the matrix method to solve the equations. In an exam, a zero determinant on a 2×2 you were told is invertible usually signals an arithmetic slip, so recheck your ad − bc.
Which numbers do I multiply for a 2×2 determinant?
For (a b; c d), multiply the main diagonal a×d, then subtract the other diagonal b×c, giving ad − bc. Watch the minus sign carefully with negative numbers, since a mistake here changes the sign of the whole answer.