1.4_1.5 - MATH1850U/2050U: Chapter 1 cont 1 LINEAR SYSTEMS...

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MATH1850U/2050U: Chapter 1 cont… 1 LINEAR SYSTEMS cont. .. Inverses and Algebraic Properties of Matrices (1.4; pg. 38) Recall: Earlier today, we learned how to multiply matrices. Caution: There is no Commutative Law for matrix multiplication! In other words, it is NOT necessarily true that AB and BA will be equal. Example: Verify that BA AB for the matrices below. Luckily, though, most of the laws for real numbers also hold for matrices. Theorem (Properties of Matrix Arithmetic): Assuming the sizes of the matrices are such that the indicated operations can be performed, the following rules of matrix arithmetic are valid. a) A B B A Commutative Law for Addition b) C B A C B A ) ( ) ( Associative Law for Addition c) C AB BC A ) ( ) ( Associative Law for Multiplication d) AC AB C B A ) ( Left Distributive Law e) CA BA A C B ) ( Right Distributive Law f) aC aB C B a ) ( g) bC aC C b a ) ( h) C ab bC a ) ( ) ( i) ) ( ) ( ) ( aC B C aB BC a Definition: A matrix whose entries are all zero is called a zero matrix . Such a matrix is often denoted by 0 or n m 0
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MATH1850U/2050U: Chapter 1 cont… 2 Theorem (Properties of Zero Matrices): Assuming that the sizes of the matrices are such that the indicated operations can be performed, the following rules of matrix arithmetic are valid. a)
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This note was uploaded on 10/12/2011 for the course MATH 1020 taught by Professor Paulatu during the Spring '11 term at UOIT.

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1.4_1.5 - MATH1850U/2050U: Chapter 1 cont 1 LINEAR SYSTEMS...

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