Lect4 - Chapter 1. Matrices and Systems of Equations...

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Unformatted text preview: Chapter 1. Matrices and Systems of Equations Math1111 Matrix Algebra More on Notation For an m × n matrix, we may write A = a ( 1,: ) a ( 2,: ) . . . a ( m ,: ) and A = a 1 a 2 ··· a n where a j : = a ( :, j ) . Chapter 1. Matrices and Systems of Equations Math1111 Matrix Algebra More on Notation For an m × n matrix, we may write A = a ( 1,: ) a ( 2,: ) . . . a ( m ,: ) and A = a 1 a 2 ··· a n where a j : = a ( :, j ) . Example . Write down the matrix A = a ( 1 ) a ( 2 ) 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 × n be a matrix and α a scalar. We define α A = α a ij m × 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 × n be a matrix and α a scalar. We define α A = α a ij m × n . Question: What is the size of the matrix α A ? Chapter 1. Matrices and Systems of Equations Math1111 Matrix Algebra Addition & Subtraction Definition ( Addition ) Let A = ( a ij ) m × n and B = ( b ij ) m × 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 × n and B = ( b ij ) m × 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 × n and B = ( b ij ) m × 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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Lect4 - Chapter 1. Matrices and Systems of Equations...

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