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Unformatted text preview: Chapter 1. Matrices and Systems of Equations Math1111 Matrix Algebra More on Notation For an m Ã— n matrix, we may write A = ï£« ï£¬ ï£¬ ï£¬ ï£¬ ï£¬ ï£¬ ï£¬ ï£ a ( 1,: ) a ( 2,: ) . . . a ( m ,: ) ï£¶ ï£· ï£· ï£· ï£· ï£· ï£· ï£· ï£¸ and A = a 1 a 2 Â·Â·Â· a n where a j : = a ( :, j ) . Chapter 1. Matrices and Systems of Equations Math1111 Matrix Algebra More on Notation For an m Ã— n matrix, we may write A = ï£« ï£¬ ï£¬ ï£¬ ï£¬ ï£¬ ï£¬ ï£¬ ï£ a ( 1,: ) a ( 2,: ) . . . a ( m ,: ) ï£¶ ï£· ï£· ï£· ï£· ï£· ï£· ï£· ï£¸ and A = a 1 a 2 Â·Â·Â· a n where a j : = a ( :, j ) . Example . Write down the matrix A = ï£« ï£¬ ï£ a ( 1 ) a ( 2 ) ï£¶ ï£· ï£¸ if a ( 1 ) = ( 1 2 ) and a ( 2 ) = ( 1 3 4 ) . Chapter 1. Matrices and Systems of Equations Math1111 Matrix Algebra Equality & Scalar Multiplication Definition ( Equality ) Let A and B be matrices. We define A = B if (i) they have the same size and (ii) their corresponding entries are equal. Chapter 1. Matrices and Systems of Equations Math1111 Matrix Algebra Equality & Scalar Multiplication Definition ( Equality ) Let A and B be matrices. We define A = B if (i) they have the same size and (ii) their corresponding entries are equal. Definition ( Scalar Multiplication ) Let A = ( a ij ) m Ã— n be a matrix and Î± a scalar. We define Î± A = Î± a ij m Ã— n . Chapter 1. Matrices and Systems of Equations Math1111 Matrix Algebra Equality & Scalar Multiplication Definition ( Equality ) Let A and B be matrices. We define A = B if (i) they have the same size and (ii) their corresponding entries are equal. Definition ( Scalar Multiplication ) Let A = ( a ij ) m Ã— n be a matrix and Î± a scalar. We define Î± A = Î± a ij m Ã— n . Question: What is the size of the matrix Î± A ? Chapter 1. Matrices and Systems of Equations Math1111 Matrix Algebra Addition & Subtraction Definition ( Addition ) Let A = ( a ij ) m Ã— n and B = ( b ij ) m Ã— n be matrices of same size . We define A + B : = a ij + b ij Chapter 1. Matrices and Systems of Equations Math1111 Matrix Algebra Addition & Subtraction Definition ( Addition ) Let A = ( a ij ) m Ã— n and B = ( b ij ) m Ã— n be matrices of same size . We define A + B : = a ij + b ij Definition ( Subtraction ) A B : = A +( 1 ) B Chapter 1. Matrices and Systems of Equations Math1111 Matrix Algebra Addition & Subtraction Definition ( Addition ) Let A = ( a ij ) m Ã— n and B = ( b ij ) m Ã— n be matrices of same size . We define A + B : = a ij + b ij Definition ( Subtraction ) A B : = A +( 1 ) B Example . For what B do we have A + B = A ? Chapter 1. Matrices and Systems of Equations Math1111 Matrix Algebra Addition & Subtraction...
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This note was uploaded on 04/30/2010 for the course MATH 1111 taught by Professor Dr,li during the Spring '10 term at HKU.
 Spring '10
 Dr,Li
 Math, Systems Of Equations, Equations, Matrices

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