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  3. 3. in r4 , does the set {(1, 1, 1, 0,(1, 0, 0, 0),

3. In R4 , does the set {(1, 1, 1, 0,(1, 0, 0, 0),(0, 1, 0,...

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Advance Math

3. In R4 , does the set {(1, 1, 1, 0,(1, 0, 0, 0),(0,1, 0, 0),(0, 0, 1, 1)}, span R4? In other words, can youwrite down any vector (a, b, c, d) ? R4 as a linearcombination of vectors in the given set ? Is the above set ofvectors linearly independent ?

4. In the vector space P2 of polynomials of degree ?2, find explicitly a polynomial p(x) which is not in the span ofthe set {x + 2, x2 ? 1}.

5. Let S be the subspace of P2 defined by S :={ax2 + bx + 2a + 3b : a, b ? R}, for different choicesof real numbers a and b (you don’t need to show here that S isindeed a subspace, and can assume. But is a good practice problem).Find a basis, and hence dimension for S.

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