Question
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Which of the following sets is a subspace of Pn for an appropriate value of n? All polynomials of the form p(t) - a + bt2, where a and b are in R All polynomials of degree exactly 4, with real coefficients All polynomials of degree at most 4, with positive coefficients A and B C only A only B only Does the vector u belong to the null space of the matrix A? u = [-2 -2 1], A = [ ] Yes No Use coordinate vectors to test whether the following set of polynomials span P2. Justify your conclusion. -3t + t2, l - 8t + 5t2, 1 + t2, -2 - 7t + 2t2 Does the set of polynomials span P2? Yes; since there is a pivot in each row, the original four column vectors spans R3. By the isomorphism between R3 and P2 , the given set of polynomials spans P2. Yes; since there is a pivot in each row, the original four column vectors spans R2. By the isomorphism between R2 and P2, the given set of polynomials spans P2. No; since there is not a pivot in each row, the original four column vectors does not span R2. By the isomorphism between R2 and P2 , the given set of polynomials does not span P2. No; since there is not a pivot in each row, the original four column vectors does not span R3. By the isomorphism between R3 and P2 , the given set of polynomials does not span P2. Determine if the vector u is in the column space of matrix A and whether it is in the null space of A. u = [-4 2 4 5], A = [ ] The vector u is not in Col A, but in Nul A. The vector u is in Col A, but not in Nul A. The vector u is not in Col A, and not in Nul A. The vector u is in Col A, and in Nul A. Find the coordinate vector [x]B of the vector x relative to the given basis B. b1 = [1 4], b2 = [5 -5], x = [-17 32], and B = {b1, b2} [x]B = [3 -3] [x]B = [-17 32] [x]B = [143 -228] [x]B = [3 -4] Which of the sets of vectors below are linearly independent? A.The set {sin t, tan t} in C[0, l]. The set {sin t cost,cos2t} in C[0, l]. The set {cos2t, 1 + cos 2t} in C[0, 1]. A and C A only A and B C only B only
Explanation / Answer
1)d
2)a
3)d
4)c
5)c
6)b
