Unformatted text preview: 4. Show that ±:² ³ → ℝ ´ defined by ±µ¶ + ·¸¹ = µ¶ − ·,·¹ is an isomorphism. Can you find the basis that this isomorphism is based on? 5. Check if the following are isomorphisms: a) ±µ¶ ³ ,¶ ´ ,¶ º ¹ = ¶ ³ + µ¶ ³ + ¶ ´ ¹¸ + µ¶ ³ + ¶ ´ + ¶ º ¹¸ ´ b) ±µ¶ ³ ,¶ ´ ,¶ º ¹ = ¶ ³ + µ¶ ³ + ¶ ´ ¹¸ c) ±µ¶ ³ ,¶ ´ ,¶ º ¹ = µ¶ ³ + ¶ ´ ,¶ ´ + ¶ º ,¶ º + ¶ ³ ,¶ ³ + ¶ ´ + ¶ º ¹ d) ±µ¶ ³ ,¶ ´ ,¶ º ¹ = µ¶ ³ + ¶ ´ + ¶ º ,¶ ³ + ¶ ´ ,¶ ³ + ¶ ´ ¹...
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 Spring '08
 staff
 Linear Algebra, Matrices, Vector Space, basis, Isomorphism, Dual space

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