Question

linear algebra please show work and steps

16. Determine if the vector = an D= (2 2 is a linear combination of the vectors: u; - and uz = 11 17. Determine if the vector 5 = 8 is in the span of the columns of the matrix. A = 5 112) Ecos 2 6 10 3 7 11) 19 18. Determine if the sets of vectors -5 are linearly independent. If the sets are linearly dependent, find a dependence relationship between the vectors. /:00)

Answer 1

16. Giren, 3 2 AT ور fc2 1 ون al -1 0 Now we get from , C = 3 CitC222 C2 = -1 4 เทา (1) and ₂ Now we put the values, of we get, 0 -1 1 3 3 2 -1 Alul . 19 3 is a 2 3u1 + (-) uz Therefore the vector 2 linear Combination of the ve the rectory w = 1:] and u why

4 17 Guren, > 8 12 3 Giren, matrix A 2 6 7 con 5 il 9 10 Now, 2 + b + c co 3 6 all 10 8 12 at 2 b + 3cz 4 2 sa tbbt7e 28 3 qat 10b tile = 12 row from ☺ we get de 3 we get 8 3) -12 4-2b-3€ putting this this value in 5(4-26-3C) +66+7e & 20-106 -15cfbb47C --46-86-8-20 4b-80 46+ 8C =12 b+ 20 = 3 b>3-2c and 9/4 - 26-36) +lob te=12 & 36-18 b-27e +10b tl1c212 8 b- 160 212-36 2-24 مل n 5

If we take b=-3 ca 6 2 2 3 and a = +-263) – 33 4+6-9 2 = a=1 bz-3 C 2 3 - 3 + 3 4 So 1 3 7 1 ]: 1 6 10 8 5 12 9 span So the rector D is the the columing of the matrix A. of

-4b-40 + 3bte=0 or b- 3 C = 0 and, 4b-4c4b-5020 os, -3b-9c=0 or, -b-3e Therefore b+ 3C20 3c on b e = then If we we take bal a = putting this value in @ we get --2-(2x++) 2-2+2 33 = -6+2 3 1) ܚܳܐܝ 3 3 Therefore, a=- b z c = -1/3 2 2 ti 1 / 2 *]*+)[]• [1]