Science:Math Exam Resources/Courses/MATH307/April 2006/Question 06 (c)
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Question 06 (c) 

Determine if each of the following statements is true of false. Show reason or proof if true and show reason or counter example if false. Let U,V,W be three subspaces of . If and , then . 
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Hint 

Science:Math Exam Resources/Courses/MATH307/April 2006/Question 06 (c)/Hint 1 
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Solution 

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Please rate my easiness! It's quick and helps everyone guide their studies. False. Proof by counter example. In the case that U = W, then it is not necessary that but instead parallel, for example in the case let , part of subspace U and an element of subspace V, it is clear that , hence , now let , part of subspace W. but , hence U is not perpendicular to W. 