Matrices and Determinants
Interactive exploration of matrix operations and determinants
Explore matrix operations and calculate determinants by interacting with the matrix cells below. Visualize how the determinant changes as you modify the matrix values!
Determinant:
0
2×2 Matrix
Current Calculation:
For a 2×2 matrix:
det(A) = a·d - b·c
For a 3×3 matrix (Sarrus rule):
det(A) = a(ei−fh) − b(di−fg) + c(dh−eg)
Understanding Matrices and Determinants
Key Concepts:
Matrices are rectangular arrays of numbers with important applications in mathematics and science:
- The determinant is a scalar value that can be computed from a square matrix
- Determinants have geometric interpretations (scaling factor of linear transformations)
- A zero determinant indicates the matrix is not invertible (singular)
- Determinants are used in solving systems of linear equations, finding eigenvalues, and more
Visual Interpretation:
For a 2×2 matrix, the determinant represents the area scaling factor of the transformation:
- Positive determinant: preserves orientation
- Negative determinant: reverses orientation
- Zero determinant: collapses space into lower dimension
For 3×3 matrices, it represents volume scaling.
