Let U be a subspace of the vector space V , let y ∈ V and define the set y + U = {v ∈ V | v = y + u for some u ∈ U}. Show that y + U is a subspace of V if and only if y ∈ U.

Q: (a) A: va+v. (b) A: (av). (c) A: √ av.

A: “Since you have posted a question with multiple sub parts, we will provide the solution only to the…

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Q: Zero is the only vector in an inner product space V that is orthogonal to itself. O True False

A: The statement is true. We give the justification in the next step.

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A: here we can use linear combination to prove that given set is linearly independent.

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