1. Show that the set of all polynomials of deg=2 is not a vector space over...

1. Show that the set of all polynomials of deg=2 is not a vector space over reals.

can this be fixed, can we have a set of polynomials that is a vector space over reals?

2. Show that the set of 2x2 matrices with m_22 = 1 is not a vector space over reals.

3. Show that the set of infinitely-differentiable real functions is a a vector space under pointwise function addition, and pointwise scalar multiplication as defined in class, is a vector space over reals.

4. Show that the set of infinitely differentiable real functions such that f(0)=2, is not a vector space over reals.

please answer 1-4 thankyou

Expert Solution

Colby Messinger answered 1 year ago

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Consider the vector space P2 of all polynomials of degree less than or equal to 2...

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Let P2 be the vector space of all polynomials of degree less than or equal to...

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