Determine which of the following are subspaces of R^3; for those which are subspaces, find a basis and write down the dimension of the subspace:
i) {(x, y, z) E R^3 : x = y = 0}
ii) {(x, y, z) E R^3 : y = 2z = 4}
iii) {(x, y, z) E R^3 : y = 3x + 4z}
iv) {(x, y, z) E R^3 : [5^(1/2)]y + [7^(1/2)]z = 0}
i.e. "E" denotes "in the interval of"
subspace
2008-04-20 3:36 pm
回答 (1)
2008-04-22 4:03 am
✔ 最佳答案
(i) is a subspace. A basis is {(0,0,1)}(ii) is not a subspace, because (0,0,0) is not in it.
(iii) is a subspace. A basis is {(1,3,0),(0,4,1)}
(iv) is a subspace. A basis is {(1,0,0),(0,1, -(5/7)^(1/2) )}
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