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Unformatted text preview: Chapter 1. Matrices and Systems of Equations Math1111 Matrix Algebra Linear Combination  Geometric Meaning Example . For what a 1 , a 2 and b will the system ¤ 2 x 1 + 3 x 2 = 8 5 x 1 4 x 2 = 7 be expressed in the form of x 1 a 1 + x 2 a 2 = b ? Chapter 1. Matrices and Systems of Equations Math1111 Matrix Algebra Linear Combination  Geometric Meaning Example . For what a 1 , a 2 and b will the system ¤ 2 x 1 + 3 x 2 = 8 5 x 1 4 x 2 = 7 be expressed in the form of x 1 a 1 + x 2 a 2 = b ? Geometric Interpretation Solving the system passes to expressing b as a sum of a 1 and a 2 after “suitable” scaling. Chapter 1. Matrices and Systems of Equations Math1111 Matrix Algebra Linear Combination  Definition Definition Let a 1 , a 2 , ··· , a m be vectors in R n , and c 1 , c 2 , ··· , c m be scalars. Then a sum of the form c 1 a 1 + c 2 a 2 + ··· + c m a m is called a linear combination of the vectors a 1 , a 2 , ··· , a m ....
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 Fall '10
 S.C

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