Let V be the set of ordered pairs (a, b) of real mumbers with addition in V and scalar multiplicat ion on V defined by (a, b) + (e, d) = (a+ c, b+d) k(a, b) = (ka, 0) and Show that V satisfies all the axioms of a voctor space except [M4-that is, except lu = u. Hence, [M4] is not a consequence of the other axioms.

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A: The complete solutions are given below

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A: In the given problem we verify the properties of vector addition

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Q: 9) Suppose u, v € V, where V is an inner product space, and ||u|| = ||v|| = 1 and (u, v) = 1. Find u…

A: I have used the property of norm,  IIxII=0 off x=0

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Q: Please see image

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Q: 1. Show that V = R? is not a vector space over R with respect to the operations: (a, b) + (c, d) =…

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Linear Algebra

In mathematics, problems can be solved by the arithmetic operators like addition, subtraction, multiplication, and division. In algebra, we represent the numbers by any letter called a variable. If these variables are of degree 1, then it is studied under linear algebra. The first-degree equations involving algebraic expressions are called linear equations. That is, if you represent it by drawing a graph you will get a straight line.