Question One

Thursday, 1 November 2018

3:26 PM

Untitled picture.png Machine generated alternative text: 1. i) Evaluate each of the following integrals. a) 11 Ink Drawings Ink Drawings Ink Drawings Ink Drawings    
Untitled picture.png Machine generated alternative text: Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Untitled picture.png Machine generated alternative text: dc 2) Ink Drawings Ink Drawings Ink Drawings Ink Drawings                        Ink Drawings Ink Drawings Ink Drawings Ink Drawings  Ink Drawings Ink Drawings Ink Drawings Ink Drawings                            
Ink Drawings Untitled picture.png Machine generated alternative text: ii) Find the general solution of the differential equation d2y dy + 2 — + 231 ¯ 2'X. dX2 dx Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings                Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings   Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings            Ink Drawings Ink Drawings Ink Drawings Ink Drawings    
Untitled picture.png Machine generated alternative text: 1 iii) Let VI = -6 -8 1 and v3 — 2 1 -2 —1 1 a) Write v3 as a linear combination of VI and v2. b) Does there exist a linear map T : such that T(VI) — and T(V3) - c) What is the relationship between span(vl, v2) and span(vl, v2, v3)? Ink Drawings                    
Untitled picture.png Machine generated alternative text: 1 iii) Let VI = -6 -8 1 and v3 — 2 1 -2 —1 1 a) Write v3 as a linear combination of VI and v2. b) Does there exist a linear map T : such that T(VI) — and T(V3) - c) What is the relationship between span(vl, v2) and span(vl, v2, v3)? Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings    Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings    Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings
Untitled picture.png iv) Let S — {x e IR3 : x2 a) Prove that S is closed under scalar multiplication. b) Show that S is not a subspace of Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings     Ink Drawings Ink Drawings Ink Drawings     Ink Drawings Ink Drawings Ink Drawings  
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