6. On Linear Independence vectors in R\" (a) Let S-{(1, 1), (?, ?)} . Îs S linea

Question

6. On Linear Independence vectors in R" (a) Let S-{(1, 1), (?, ?)} . Îs S linearly independent of not? (b) Let S = {(1, 1), (?, 0)}. Is S linearly independent of not? (c) Let S-(1,0,0), (0, 1,0), (0, 0,1)). Is S linearly independent of not? (d) Let S-{(1,0,0,0), (0, 1,0. ?),(0,0,1), (0.0.0.1)). Is S linearly (e) Let S-(1,1,1), (1,-1,1), (1,1,-1)). Is S linearly independent (f) Let S (1,0,1), (1,2,1), (1,2,2), (13,17,19)j. Is S linearly in (g) Let S - [(1,1,1), (1,2,1), (0, 1,0), (3,4,3)). Is S linearly inde- independent of not of not? dependent of not? pendent of not?

Explanation / Answer

1. Dependent as other vectoris pi times of the (1,1)

2. Independent, cant express each other using them.

3.Independent, as this set is basis for R3.

4. 3rd vectoris not written properly, if the 3rd vector id (0,0,1,0) then it is indeendent.

5. independent the set is nothing but the basis vector with some manupulation.

6. Dependent , as These are vector from R3 and the set has 4 vector.

7.same as 6, dependent

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