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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

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