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Unformatted text preview: THE CHINESE UNIVERSITY OF HONG KONG Department of Mathematics MATH2510 Linear Algebra and Applications (Winter 2011) Homework 3 Due Date: 25 th February, 2011 Name: Student No.: Class: Final Result: I acknowledge that I am aware of University policy and regulations on honesty in academic work, and of the disciplinary guidelines and procedures applica- ble to breaches of such policy and regulations, as contained in the website http://www.cuhk.edu.hk/policy/academichonesty/ Signature Date Answer all the questions. 1. (Optional) In Problems (a) and (b), a set of objects is given together with addition operator + and scalar multiplication operator • . Determine which sets are vector spaces under the given operations. For those that are not, list all axioms that fail to hold. (a) The set of all positive real numbers u with the operations u + v = uv and k • u = u k . (b) The set of all ordered pairs of real numbers with the operations ( x, y )+( x ′ , y ′ ) = ( x + x ′ , y + y ′ )...
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