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2. Matrix Algebra

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

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2. Matrix Algebra

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  1. 2. Matrix Algebra 2.1 Matrix Operations

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

  3. 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.

  4. Example:

  5. Example:

  6. REVIEW Matrix Multiplication Recall:

  7. Matrix Multiplication Example: Let

  8. 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

  9. Properties of Matrix Multiplication

  10. 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 ?

  11. Rules related to transpose:

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