Matrix Operations and Applications
This page introduces fundamental concepts of matrix operations and their properties. It covers various types of matrices and basic operations such as addition, subtraction, and multiplication.
Definition: A zero matrix is a matrix where all elements are zero.
Definition: An identity matrix is a square matrix with ones on the main diagonal and zeros elsewhere.
The page explains how to multiply matrices, emphasizing that matrix multiplication is only possible when the number of columns in the first matrix equals the number of rows in the second matrix.
Highlight: Matrix multiplication is not commutative, meaning AB ≠ BA in general.
Multiplying matrices 2x2 is demonstrated with examples, and the concept of determinants is introduced for 2x2 matrices.
Example: For a 2x2 matrix, the determinant is calculated as detM = ad - bc, where M = ab;cd.
The page also touches on the concepts of singular and non-singular matrices, which are important for understanding matrix invertibility.
Vocabulary: A matrix is singular if its determinant is zero, and non-singular if its determinant is non-zero.
Finally, the page introduces the concept of matrix inverses, noting that for non-singular matrices A and B, AB⁻¹ = B⁻¹A⁻¹.