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Unformatted text preview: THE CHINESE UNIVERSITY OF HONG KONG Department of Mathematics MAT2510 Linear Algebra and Applications (Winter 2011) Homework 6 Name: Student No.: Class: Final Result: I acknowledge that I am aware of University policy and regulations on hon- esty in academic work, and of the disciplinary guidelines and procedures appli- cable to breaches of such policy and regulations, as contained in the website http://www.cuhk.edu.hk/policy/academichonesty/ Signature Date Due Date: 28th April, 2011 Answer all the questions. 1. Find a basis for (a) the column space of A T , (b) the null space of A T , (c) the column space of A , and (d) the null space of A for each of the following matrices: (i) A = 5 2- 1 2 4 1 1 4 (ii) A = 1 1 2 2 0 0 1 0 0 4 8 0 0 0- 4 0 2. Write v = u + w with u in U and w in U ⊥ in each of the following situations. (a) V = R 2 , v = bracketleftbigg x y bracketrightbigg , U = braceleftbiggbracketleftbigg t t bracketrightbiggvextendsingle...
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