Homework 12 Solutions - MATH 110 Spring 2015 Homework 12...

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MATH 110 Spring 2015 Homework 12 Solutions 6.1 6.1.5
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6.1.13 We could check all the axioms for an inner product. For any x, y, z V and any scalar c , < cx + y, z > = < cx + y, z > 1 + < cx + y, z > 2 = c ( < x, z > 1 + < x, z > 2 ) + ( < y, z > 1 + < y, z > 2 ) = c < x, z > + < y, z > . < x, y > = < x, y > 1 + < x, y > 2 = < y, x > 1 + < y, x > 2 = < y, x > . < x, x >

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