Question

1. Consider the vectors: (a) Determine if b = 0 is a linear combination of a, a, and a bi (b) Determine the set of values of b1,b2, bg such that b2 is not a linear combination of a as, and 2. Explain why the nullspace of R the same as that of M, where R is the RREF of M.

please show work. thank you

Answer 1

Olet Baga+86 + then. [3]=439 where 0.9,9 me scalars. ..2 1 2 = -39, + 4 4 + 65 09 - - 4 = 24-89-49----- solving this system of linear equations we get 9 $ frm@] I 2=-30, +46 +60 (from 0507 > 39 +49 = 2 ----- & 4 = 26-84-4C, [from 9 &0) - C - 42 = 2 From I we get 29=9 G=2 { "2 - 49=2 = =-) G=2 = ust z=2 Therefore is a linen combination of an a D B222-+293. we to check , in linearly independe or not For this Blet, car +49 +593 = 0, whore e, aga [3]*[8)*8197=6

= -39 +49 +62 = 0 & erg=0 & 29-84-99 = 0 solving this system of lineer equation weget @aç & 39 +44 =0 f-9-99 20 solve this we get 9, 20, 90, 920 1, 2, az is linearly independent. and this set a vectors span R & as dimension of s= {1, 2, 3 i 3 and dim C1R3) 23. The rebore & these set a ceckrs is a basis a 183 if any vector can be written as a linear combinat & Bu az. so there is no vector which is end not linear combination of a 8 az