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Unformatted text preview: vector space (see chapter 4). 1.2. Some multiplication properties. Some more properties involving multiplication: Theorem 2. ( AB ) C = A ( BC ) ( A + B ) C = AC + BC and A ( B + C ) = AB + AC 1.3. Things which fail. However, here are some things which are FALSE! : It is not true that AB = BA . For example, 1 0 0 0 0 1 0 0 6 = 0 1 0 0 1 0 0 0 AB = 0 doesnt mean that either A = 0 or B = 0, for example 0 1 0 0 1 0 0 0 = 0 0 0 0 AB = AC might be true even if B 6 = C and A 6 = 0. For instance 1 0 0 0 1 1 1 1 = 1 0 0 0 1 1 0 0 but 1 1 1 1 6 = 1 1 0 0 1 (so you cant just cancel the matrix) 1 0 0 0 1.4. Algbraic properties of the transpose. Theorem 3. ( A T ) T = A ( A + B ) T = A T + B T ( AB ) T = B T A T NOTE THIS ONE CAREFULLY!!! ( rA ) T = rA T 2...
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 Spring '08
 Bens
 Linear Algebra, Algebra, Matrices

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