Consider two subsets of R 3 given as, S 1 = {[2, 3, 1], [1, 0, 5], [0, 1, 0], [0, 0, 1]} and S 2 = {[1, 0, 0], [0, 1, 1], [0, 0, 0]}. Which of the following statements is true?

Correct Answer is : Both S1 and S2 are linearly dependent.

1 is linearly dependent but S 2 is linearly independent.

Both S 1 and S 2 are linearly independent.

S 1 is linearly independent but S 2 is linearly dependent.

Both S 1 and S 2 are linearly dependent.

AAI ATC Junior Executive 2018 Shift 1 Paper

Question : 119 of 120

Marks: +1, -0

Consider two subsets of R³ given as,
S₁ = {[2, 3, 1], [1, 0, 5], [0, 1, 0], [0, 0, 1]} and S₂ = {[1, 0, 0], [0, 1, 1], [0, 0, 0]}. Which of the following statements is true?

1 is linearly dependent but S₂ is linearly independent.
Both S₁ and S₂ are linearly independent.
S₁ is linearly independent but S₂ is linearly dependent.
Both S₁ and S₂ are linearly dependent.

Validate

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