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Answer each one, with (brief) justification. Throughout, V denotes a vector space, and bold-face letters like u,...

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Advance Math

Answer each one, with (brief) justification. Throughout, Vdenotes a vector space, and bold-face letters likeu, v, etc denote vectors inV.

A1. Suppose there are three linearly independent vectors in V.Is V necessarily finite-dimensional?

A2. Suppose there are three vectors in V that span V. Is Vnecessarily finite-dimensional?

A3. What is the dimension of the vector space of all polynomialsof degree 4 or less?

A4. Can an infinite-dimensional vector space contain afinite-dimensional subspace?

A5, In a finite-dimensional vector space, is every spanning setnecessarily finite?

A6. Can R3 contain a four-dimensional subspace?

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