HW2 - Z b a fg = ±Z b a f ² ±Z b a g ² Prove it or...

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MATH 186 – WINTER 2009 HOMEWORK SET 2 Due Friday 01/30 Be kind to your grader, please staple your work! What you need to know: - Some discontinuous functions are integrable! - Fundamental Theorem of Calculus (FTC) - Operations with matrices What you shouldn’t forget: - Definition of integrable functions - Vectors and matrices Ex 1. Let f,g : [ a,b ] R be two integrable functions. Is it true that
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Unformatted text preview: Z b a ( fg ) = ±Z b a f ² · ±Z b a g ² ? Prove it, or find a counterexample. Ex 2. Let A be an 3 × 3 matrix with real coefficients, and let ~x and ~ y be two vectors. Suppose that A~x = A~ y. Does this imply that ~x = ~ y ? Prove it or find a counterexample. From Spivak: Chapter 13: Ex # 26, 28. Chapter 14: Ex # 6. Please recycle!...
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