Linear Algebra
The two by two base case
Main diagonal minus the off diagonal, the shortest determinant rule.
The Formula
det = a x d - b x c
Main diagonal minus the off diagonal, the shortest determinant rule.
| Symbol | Meaning | Unit | Notes |
|---|---|---|---|
| det | Determinant | unitless | The signed scale factor of the matrix. |
| a, d | Main diagonal | unitless | The entries running from top left to bottom right. |
| b, c | Off diagonal | unitless | The entries running from top right to bottom left. |
What Each Symbol Means
detunitless
Determinant
The signed scale factor of the matrix.
a, dunitless
Main diagonal
The entries running from top left to bottom right.
b, cunitless
Off diagonal
The entries running from top right to bottom left.
See It Worked With Real Numbers
A formula on its own does not tell you which number goes where. The how to calculate a matrix determinant page applies this equation to a concrete case, shows every intermediate step, and names the mistakes that produce a wrong answer even when the algebra is right.
Where This Formula Appears
This equation is the working core of How To Calculate A Matrix Determinant, filed under Math. Every number the guide produces comes from substituting into this one line.