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Unformatted text preview: NOTES ON SECTION 1 . 3 MA265, SECTIONS 41, 52 Key words Dot product Coefficient matrix inner dimensions Matrix product augmented matrix Given two nvectors (they have to be the same size), the dot product is defined as the obvious general ization of this example: [1 , 4 , 2 ,π ] · 1 2 1 2 = 1 * (1) + ( 4) * 2 + 2 * 1 + π * 2 = 5 + 2 π Given two matrices A = a 11 a 12 ... a 1 n a 21 a 22 ... a 2 n a 31 a 32 ... a 3 n . . . . . . . . . a m 1 a m 2 ... a mn ,b = b 11 b 12 ... b 1 p b 21 b 22 ... b 2 p b 31 b 32 ... b 3 p . . . . . . . . . b n 1 b m 2 ... b np the matrix product A * B is the matrix with i,jentry equal to n X k =1 a i,k * b k,j i.e. it is the “dot product” 1 of the i th row of A and the j th column of B . It only makes sense if the inner dimensions are equal: A = m × n and B = n × p , and the product makes sense because “...
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This note was uploaded on 03/31/2012 for the course MA 265 taught by Professor Bens during the Spring '08 term at Purdue.
 Spring '08
 Bens
 Linear Algebra, Algebra, Vectors, Dot Product

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