Question

Problem 2 (16 points) Consider the town was ------ - 0 1. Pla de Il for K, that is compond with vectors in K. 2. What is the son of the vector pe V-pank) in the coordinate vector in of - [ ]

Answer 1

Problem: 2 k = 4W;, 62,Wy , ? 1. We check whether the vectors O,,U2, Uz are linearly determinant in dependent of not, we calculate the 3 2 - 2 is = 3.4 – 2:3+1.67) = 12-6-7 = -1 70 linearly this shows the vectors ", U2, U3 are & independent, GIR², since B = 74,, U2, 6,} is a k C so, basis for K. V 2. So, So, the dimension of the vector space = span (k) is 3 = CS Scanned with Carmen

3. Let 9 t2 23일 ? - then 3 2. + 2. 5 4 2. SO , 34 +22 431 2 (4 + 5, - (9, = 2.- 9 모 +3 " 3 Now, + (2) and (2) + gives 59+7 =3 and 3qt42 = 3 NOW, so, C = 3-7(-6) 15 A+ 21p = q Gt202 = 15 6 5 2 = from ③ S 1 - C - Go = 1 -4-(6) 4-14 So, 9, 2 = -6, s = -14 thus [], 9. - 6 -11 Ics