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  3. 4 10 points show that the set of vectors in...

Question: 4 10 points show that the set of vectors in...

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4. (10 points) Show that the set of vectors in R2 of the form (r, y) with r >y is not a subspace of R?. For example. (2. 1) is in this collection, but (3.4) is not. Give an explicit counterexample of this set behaving badly, to demonstrate this fact. The counterexample should use actual numbers. although simple numbers should work. You just have to find one of the following ways in which this collection of vectors behaves badly (a) If the zero vector 0 (0,0) breaks the rule, show that, and this cant be a subspace. (b) Or you could look for two vectors, u and v. both of that form, so that when you add them together you get w u v, where w is not of the required form. (c) Or you could try to find a find a vector u that is of this form and a scalar value k such that ku is not of that form. One explicit counterexample (with actual numbers) is sufficient. The vector or vectors used must satishy the restriction (in this case, that a ) and the result of the operation (scaling or adding) must fail to satisfy the restriction, showing that this collection is not closed under the operation the way it is supposed to be for a subspace.
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