chapter3.page03

chapter3.page03 - 1 VECTORS AND MATRICES 3 and B= 0 5 3-4...

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Unformatted text preview: 1. VECTORS AND MATRICES 3 and B= 0 5 3 -4 , find (a) A + B, (b) 3A, (c) 4A - B. Solution (a) A+B = = (b) 3A = 3 (c) 4A - B = 8 12 -4 16 - 0 5 3 -4 = 8 7 -7 20 2 3 -1 4 = 6 9 -3 12 2 3 -1 4 + 0 5 3 -4 = 2 8 2 0 2+0 3+5 -1 + 3 4 + (-4) The following fact lists all properties of matrix addition and scalar product. Theorem 1.1. Let A, bB, and C be matrices. Let a, b be scalars (numbers). We have (1) A + 0 = 0 + A = A, A - A = 0; (2) A + B = B + A (commutativity); (3) A + (B + C) = (A + B) + C, (ab)A = a(bA) (associativity); (4) a(A+B) = aA+aB, (a+b)A = aA+bA (distributivity) When we have a row vector and a column vector with the same number of elements, we can define the dot product as Definition 1.2. Dot Product: in 2-dimension: Let x = dot product of x and y is, x y = x1 y1 + x2 y2 x1 x2 and y = y1 , the y2 ...
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This note was uploaded on 10/04/2011 for the course MAP 4231 taught by Professor Dr.han during the Spring '11 term at UNF.

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