Determinant
- 2 × 2: for the matrix [a b; c d], the determinant is ad − bc.
- 3 × 3: the calculator expands along the first row (cofactors), which gives the same result as the rule of Sarrus.
Example
For [4 7; 2 6], the determinant is 4 × 6 − 7 × 2 = 10, and the inverse is [0.6 −0.7; −0.2 0.4].
The 3 × 3 matrix [2 1 1; 1 3 2; 1 0 0] has determinant −1, so it has an inverse.
Inverse matrix
A matrix has an inverse only when its determinant is not zero. The inverse is the transpose of the cofactor matrix divided by the determinant. Multiplying a matrix by its inverse gives the identity matrix.
Frequently asked questions
What is a singular matrix?
A square matrix with determinant 0. It has no inverse, and a system of equations with it has no single solution.
What is the transpose?
The matrix with rows turned into columns: the element in row i, column j moves to row j, column i.
What is the trace?
The sum of the numbers on the main diagonal, from the top left to the bottom right.
See also
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