Math_LinAlg - A brief review of Linear Algebra and Linear...

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MIT and James Orlin © 2003 1 A brief review of Linear Algebra and Linear Programming Models

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MIT and James Orlin © 2003 2 Review of Linear Algebra Some elementary facts about vectors and matrices. The Gauss-Jordan method for solving systems of equations. Bases and basic solutions and pivoting.
MIT and James Orlin © 2003 3 Elementary Facts about Vectors 1 2 3 4 v v v v v is called a row vector . 1 2 3 4 t v v v v v The transpose of v is a column vector . 1 2 3 4 w w w w w is another row vector. The inner product of vectors w and v is given by: 1 1 2 2 3 3 4 4 v w v w v w v w v w o

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MIT and James Orlin © 2003 4 Matrix Multiplication ( ) ij A a ( ) ij B b ( ) ij C c A B 1 k kj n ik j i a b c Suppose that A has n columns and B has n rows.
MIT and James Orlin © 2003 5 Multiplying Matrices Let C = ( c ij ) = AB. Then c ij is the inner product of row i of A and column j of B .

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