chapter3.page03

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

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1. VECTORS AND MATRICES 3 and B = 0 5 3 - 4 , find (a) A + B , (b) 3 A , (c) 4 A - B. Solution (a) A + B = 2 3 - 1 4 + 0 5 3 - 4 = 2 + 0 3 + 5 - 1 + 3 4 + ( - 4) = 2 8 2 0 (b) 3 A = 3 2 3 - 1 4 = 6 9 - 3 12 (c) 4 A - B = 8 12 - 4 16 - 0 5 3 - 4 = 8 7 - 7 20 a 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 ) (associa- tivity);
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