Question

Which of the following is linearly independent subset of R3? Select one: O a. O b. 1 1 {[1 2 3] 3], [ 2 0],[1 0 0} {[1 2 4] [3 4 0], [5 1 1],[o 1 ]} oc{lo o o].[1 1 2]} o].[O O d. 2 3

Answer 1

R3² R3 R2 linearly independent subset of R3 ca). 5={[1,2,3],[1,2,0],[1,0,073 s can be written in matrix form operating 2 3 2 and R 3 R3-R, R2² R2-R, "{:: o 2 3 in Rank (5)=3 = order of linearly independent. = ) S is (6). dim (R₂) = 3 So set {(1,2,4], [3, 4, 0], [5, 1,1], [0, 1, 0]} set having element greater then dimension of vector spsce depend So is CS Scan the wita CamScaalways

- C) 5+ { [0,0,0], [0,1,2) } element 'o' zero Set containing always is dependent (d) $= {[1,2,3],[1,1,0], [0, 1, 13] § that 1st element is linear combination cal to thes we see how two. [1,2,3] =![lol,0] + [0, 1, 3) 1 ['s 1,0) + Co, 1, 3] 2 [1, 2, 3] dependent a 5 is true. so only (a) is CS Scanned with Cam Scanner