Determinants

Math

Definition

The determinant is a scalar value computed from a square matrix that indicates whether the matrix is invertible and describes the scaling factor of the linear transformation it represents. A determinant of zero means the matrix has no inverse.

Examples

  • For matrix [[a,b],[c,d]], det = ad - bc
  • A 2×2 matrix [[3,1],[2,4]] has determinant 3(4) - 1(2) = 10
  • Determinants are used in Cramer's rule to solve systems of equations
Key Fact

For a 2×2 matrix: det[[a,b],[c,d]] = ad - bc

Related Terms

Matrix operations Inverse matrices Solving systems with matrices

Study This Concept

Practice determinants with free review games in these units:

Pre-Calculus Unit 7: Systems and Matrices