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**Unformatted text preview: **University of Toronto at Scarborough Department of Computer & Mathematical Sciences MAT A23 Winter 2008 Lecture 5 Sophie Chrysostomou 1.3 Linear Systems and Matrices Matrices Addition Subtraction and Scalar Multiplication definition 0.1. Let A = [ a ij ] and B = [ b ij ] be m × n matrices and k be a scalar then: i) A + B is defined to be the matrix with ij th entry ( A + B ) ij = a ij + b ij ii) A- B is the matrix with ij th entry ( A- B ) ij = a ij- b ij iii) kA is the matrix with ij th entry ( kA ) ij = k a ij A matrix with zero entries only is called, a zero matrix and is denoted by O . example 0.2. Let A = 2- 1 3 2- 2 4 and B = 1 3- 2- 5 6- 7 . Find A + B and 2 A- 3 B . 1 definition 0.3. Let A be an n × m matrix and B be an m × k matrix. Then AB is defined to be the n × k matrix with the ij th entry given by ( AB ) ij = ( i th row of A ) · ( j th column of B ) . Letting a i be the i th row of A and b j be the j th column of B , then AB = -- a 1---- a 2-- ....

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