Determine whether S is a basis for the indicated vector space. S = {(0,4, -1), (5,...
Question 4 2 pts Determine whether the vector u is in the column space of the matrix A and whether it is the null space of A. 1 0 3 1 -2 1 - 4 U = 3 3 0 4 - 1 3 6 Not in Col A in Nul A In Col A, not in Nul A Not in ColA, not in Nul A In Col A and in Nul A Question 5 1 pts 1 co 2...
Determine if each basis is orthogonal. Further, is the basis orthonormal? (a) In the vector space R3 (i.e. column vectors in 3-space): -1 1 ( 2 5 3 -3 (b) In the vector space that consists of polynomial functions of degree less than or equal to 2: {f(x) = x2 – 3, g(x) = 4, h(x) = x2 +2} (c) In the vector space that consists of 2x2 matrices: (You'd decided what the inner product was on a previous math...
5. (a) (7 marks) Determine whether the following sets form a basis for R3. Explain your answers. i. - {0:0} - {0:00) - {000) -*-**(0-1 1 (b) (3 marks) Is the set W = a vector space? Explain your answer.
(a) Determine a basis for the subspace of M2x2(R) spanned by A-[-1.),B=(-4c-[i 1.0- [5 1]. (b) Let S be a subspace of the vector space R3 consisting of all points lying on the plane with the equation 20 + 4y - 32 = 0. Determine a basis for S and extend it to a basis for R3.
5. Determine, with proof, whether each of the following subsets S of a vector space V is linearly dependent or independent: a) V = R. S = {(2, 8.-1.4), (3.2. 4.0), (-1,-5, 2, 3), (0.0.7, 2)} 1112×2
Please finish the last part of
question 1 and question 2 as well please if you can. Thank
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Determine whether S is a basis for R3. S = {(5, 2, 4), (0, 2, 4), (0, 0,4)} S is a basis for R3. OS is not a basis for R3. If S is a basis for R3, then write u = (15, 2, 12) as a linear combination of the vectors in S. (Use S1, S2, and S3, respectively, as...
Determine whether the given S is a linearly independent subset of the given vector space, V 1. 48- 4118
Determine whether the given S is a linearly independent subset of the given vector space, V 1. 48- 4118
Find a subset of S which is a basis of the vector space V. (a) V = R3, S = = {(!),()()($).():(})} (b) V = P3(R), S = {1+ 2x, 1 + x + x2, 2+x - x2, 3+2x, * - 2x3}
2) Determine if each of the sets below is a vector space, give a basis if it is a vector space or an explanation if it is not a vector space. Зр 2q -P p +9) p.q ER {[1]: a+c=0} ; T,S, ER 2t
6. Determine if each basis is orthogonal. Further, is the basis orthonormal? (a) In the vector space R3 (i.e. column vectors in 3-space): 3 -1 2 3 1 5 -3 (b) In the vector space that consists of polynomial functions of degree less than or equal to 2: {f(x) = x2 – 3, 9(x) = 4, h(x) = x2 +2} (c) In the vector space that consists of 2 x 2 matrices: (You'd decided what the inner product was on...