Linear Algebra
Determinants
The determinant is a scalar value computed from a square matrix that reveals properties of the matrix.
Key Formulas
2×2
Determinant of a 2×2 matrix.
Key Concepts
InvertibilityCofactor expansionCramer's rule
Worked Examples
1
Solution:
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Vectors
A vector has both magnitude and direction. Vectors are fundamental in physics and linear algebra.
Matrices
A matrix is a rectangular array of numbers used to represent linear transformations and systems.
Eigenvalues and Eigenvectors
An eigenvector of a matrix is a vector that only scales when the matrix is applied. The scaling factor is the eigenvalue.