2. Matrix Algebra 2.1 Matrix Operations.

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Presentation transcript:

2. Matrix Algebra 2.1 Matrix Operations

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

Recall: Two matrices are the same 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:

Example:

REVIEW Matrix Multiplication Recall:

Matrix Multiplication Example: Let

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. Example: 3x2 2x2 3x2

Properties of Matrix Multiplication

Defn: Given an mxn matrix A, the transpose of A is the nxm matrix, denoted by AT, whose columns are formed from the corresponding rows of A. Example: Let What is AT ?

Rules related to transpose: