Question

(10 points) Are the vectors ū linearly dependent [25 1], ū = [-5 -5 o] and ū = [-5 -3 2] linearly independent? If they are linearly dependent, find scalars that are not all zero such that the equation below is true. If they are linearly independent, find the only scalars that will make the equation below true. ũ+ ö+ ū = 0.

Answer 1

Thank you for your question. I have given complete solution in the file attached. If you are satisfied with the solution, please give a thumbs up. Happy HomeworkLibing !!!

Linearly Independent definition Set of vectors is said to be Sa {x,, 42,..., an} from rector space VCF) independent If + en an=0 ₂ z linearly qat ₂ + GE On O s is to said be linearly dependent set of vectors Gd, t ₂ L₂ + ... + Cn an o atleast one lito if

Your Solution J's [2,5,1] V=[-5,-5, 0] w = [-5, -3,2 Let a, b, c be scalars in IR such that au + bitewz Ő + a ( 1, s,') + M(-s-S,9) + c(-s,-1,2)= (22-56-5c, 52-56-3c, a+2c)= (0,0,0) 20-56-50 =0 54 - 56 - 3c = o + 20 = ↑ a 2 -5 -S D 5 -5 -3 [:] Applying row echelon operations 2 с. on Y → Coefficient matrix Y R2 → 2R₂-5R 2 -5 -5 R₃ > 3 R₃-R₂ 2 5 -5 -5 -3 2 15 19 25 9 - Rg 2R ₃R, 2 -5 -5 19 we have OON 0 -5 -5 15 19 8 10-8 98 or ae linearly independent. CEO, beo, a=0 Hence 3, 5, w are only scalars that will make the equation given true are OU +0+ Ow= ie. ((0.0,o) c scanned with CamScanner