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# lecture_6 - MA 35100 LECTURE NOTES MONDAY JANUARY 25 Matrix...

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Unformatted text preview: MA 35100 LECTURE NOTES: MONDAY, JANUARY 25 Matrix Algebra You are probably familiar with adding vectors, and multiplying them by scalars: ( x 1 ,y 1 ) + ( x 2 ,y 2 ) = ( x 1 + x 2 , y 1 + y 2 ) , k ( x,y ) = ( k x, k y ) . (Recall that a scalar k is simply a real number.) The same is true for arbitrary vectors (column matrices) in R n : a 1 a 2 . . . a n + b 1 b 2 . . . b n = a 1 + b 1 a 2 + b 2 . . . a n + b n , k a 1 a 2 ··· a n = k a 1 k a 2 . . . k a n . We make the same definition for arbitrary n × m matrices. Definition. Consider two n × m matrices A and B : A = a 11 a 12 ··· a 1 m a 21 a 22 ··· a 2 m . . . . . . . . . . . . a n 1 a n 2 ··· a nm , B = b 11 b 12 ··· b 1 m b 21 b 22 ··· b 2 m . . . . . . . . . . . . b n 1 b n 2 ··· b nm . The sum of A and B is defined as that n × m matrix with entries a ij + b ij : A + B = a 11 + b 11 a 12 + b 12 ··· a 1 m + b 1 m a 21 + b 21 a 22 + b 22 ··· a 2 m + b 2 m ....
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lecture_6 - MA 35100 LECTURE NOTES MONDAY JANUARY 25 Matrix...

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