Consider two subsets of R 3 given as S 1 = {[1, -1, 2], [3, 2, -1]} and S 2 = {[2, 7, -3],[-6, -21, 9]}. Then:

Correct Answer is : S1 can be enlarged but S2 cannot be enlarged to a basis for R3

neither S 1 and S 2 can be enlarged to a basis for R 3

S 1 can be enlarged but S 2 cannot be enlarged to a basis for R3

S 1 cannot be enlarged but S 2 can be enlarged to a basis for R3

both S 1 and S 2 can be enlarged to a basis for R3

AAI ATC Junior Executive 2018 Shift 3 Paper

Question : 68 of 120

Marks: +1, -0

Consider two subsets of R³ given as
S₁ = {[1, -1, 2], [3, 2, -1]} and S₂ = {[2, 7, -3],[-6, -21, 9]}. Then:

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