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Unformatted text preview: M . i) Show that ² b a f ≤ M ( ba ) . 2 MATH 186 – WINTER 2009 HOMEWORK SET 1 ii) Show that if f is continuous on [ a, b ], then ± b a f ( x ) dx = ( ba ) f ( ξ ) , for some ξ ∈ [ a, b ]. Ex 3. Let A be the 2 × 2 matrix 1 23 4 . i) Find a vector ±v 1 such that A±v 1 = [ 1 ]. ii) Find a vector ±v 2 such that A±v 2 = [ 1 ]. iii) Find a matrix B such that AB = 1 1 . iv) What is the relationship between AB and BA in this case? From Spivak: Chapter 13: Ex # 31 (a), 37. Please recycle!...
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 Winter '08
 STAFF
 Calculus, Derivative, Vectors, Continuous function

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