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In Exercises 7–14, either use an appropriate theorem to show that the given set, W, is a
7.
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- 1. Let V be the set of all ordered pairs of real numbers, and consider the following addition and multiplication operations on -() and r-(.2): +Y (M +V+1, +v +1). ki - (ku ku) Is Va vector space? Justify your answerarrow_forwardThe given set together with the given operations is not a vector space. List the properties that fail to hold.arrow_forwardCompute the products in Exercises 1–4 using (a) the definition, as in Example 1, and (b) the row–vector rules for computer Ax, or, the rule for computing a product Ax in which the i th entry of Ax is the sum of the products of corresponding entries from row i of A and from the vector x. If a product is undefined, explain why.arrow_forward
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