Let V be a vector space and let W1 and W2 be subspaces of V. Define...

 

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Let V be a vector space and let W1 and W2 be subspaces of V. Define the following subsets of V: W1 + W2 = {w1 +w2 | w1 € W1 and w2 € W2} W1n W2 = {w€ V | WE W1 and w€ W2} W1 UW2 = {W EV | W e W1 or we W2} (a) Show that W1n W2 is a subspace of V. (b) Show that W1 + W2 is a subspace of V. (C) Let V = R 2. Show by means of an example that W1 U W2 is not necessarily a subspace of R 2. Which of the three rules is not satisfied? Let V be a vector space and let W1 and W2 be subspaces of V. Define the following subsets of V: W1 + W2 = {w1 +w2 | w1 € W1 and w2 € W2} W1n W2 = {w€ V | WE W1 and w€ W2} W1 UW2 = {W EV | W e W1 or we W2} (a) Show that W1n W2 is a subspace of V. (b) Show that W1 + W2 is a subspace of V. (C) Let V = R 2. Show by means of an example that W1 U W2 is not necessarily a subspace of R 2. Which of the three rules is not satisfied?

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The image contains a problem related to vector spaces and subspaces with three parts labeled a b and c Ill address each part of the question step by step a Show that W1 W2 is a subspace of V To prove ... View the full answer