Question

Need help please

Show that the set is linearly dependent by finding a nontrivial linear combination of vectors in the set whose sum is the zero vector. (Use S1, S2, and s3, respectively, for the vectors in the set.) S = {(3, 4), (-1, 1), (2, 0)} (0,0) = Express the vector si in the set as a linear combination of the vectors S2 and 53. $1 =

Answer 1

Geren that s = { (3,4),(-1, 1), (2,0)} Let S = (3,4) S2 = (-1,1) S3 = (2,0). for LD, if there exists a nonfreivial linear combination of S,,S2, S3 that equals to zero vectors. So, let a(3, 4) + B(-1,1)+Y (2,0) = (0,0) -) (34,4Q) + (-B, B) +(27,0) = (0,0). = 3x-ß+28 .o - - - - (1) and 42+ B + 0 0 - - - -(1). from egn (11), we get. value of Br - 49 in egner), B=-49 Putting the 30-(-4X) + 2y =0. =) 34 +44 +2y =0. - 78+24 0 = 70 =-28. » X=-Y. So, a = -2 Y , ß=-40 = - 4x-2 Y + 8y.

을 Y = Y. Now Putting Y=t, we get a = -2 B-3. Y . 220 10,0) = 곡 (3,4) + 욕 (-), ) + ) (2,0) 기 (0, 0) = - 2 3 + 록 2 +)(4). 키위 욕 S2S 50 > 2+3 키S5 글 (욕2) 1X - S, = 2 x 2 / S2 + I Sg. 키 425들