2.1 Matrix Operations 2. Matrix Algebra. j -th column i -th row Diagonal entries Diagonal matrix : a square matrix whose nondiagonal entries are zero.

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Presentation transcript:

2.1 Matrix Operations 2. Matrix Algebra

j -th column i -th row Diagonal entries Diagonal matrix : a square matrix whose nondiagonal entries are zero.

Recall: Two matrices are equal the matrices are the same size and their corresponding entries are equal. Theorem 1 Let A, B, and C be matrices of the same size, and let r and s be scalars.

Example:

Matrix Multiplication REVIEW Recall:

Matrix Multiplication Example: Let

Example: Row-Column Rule for Computing AB: If the product AB is defined, then the entry in row i and column j of AB is the sum of the products of corresponding entries from row i of A and column j of B. 3x22x23x2

Properties of Matrix Multiplication

Defn: Given an m×n matrix A, the transpose of A is the n×m matrix, denoted by A T, whose columns are formed from the corresponding rows of A. Example: LetWhat is A T ?

Rules related to transpose: