Explain why the following sets of vectors are not basis for the indicated vector spaces. (Solve this problem by inspection.)

(a) u1 = (1, 2), u2 = (0, 3), u3 = (2, 7) for R^2

(b) u1 = (-1, 3, 2), u2 = (6, 1, 1) for R^3

Question

Mathematics

Layton Summers

29 October, 05:40

Explain why the following sets of vectors are not basis for the indicated vector spaces. (Solve this problem by inspection.)

(a) u1 = (1, 2), u2 = (0, 3), u3 = (2, 7) for R^2

(b) u1 = (-1, 3, 2), u2 = (6, 1, 1) for R^3

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Marques · Answer 1

a. This set of vectors are not basis for vector space for two-dimentional space R2 due to high number of vectors (3). It means three vector is two much to span 2-dimentional space.

b. This set of vectors are not basis for vector space for three-dimentional space R3 due to small number of vectors (2). It means two vector can't span three-dimentional space.

Explain why the following sets of vectors are not basis for the indicated vector spaces. (Solve this problem by inspection.)(a) u1 = (1, 2), u2 = (0, 3), u3 = (2, 7) for R^2(b) u1 = (-1, 3, 2), u2 = (6, 1, 1) for R^3

Explain why the following sets of vectors are not basis for the indicated vector spaces. (Solve this problem by inspection.)

(a) u1 = (1, 2), u2 = (0, 3), u3 = (2, 7) for R^2

(b) u1 = (-1, 3, 2), u2 = (6, 1, 1) for R^3