Find m for which (1,-3,m) lies in the subspace spanned by (1,-1,0) and (5,-3,1) For what value of a is the set of vectors S = {(-1, 2, 5), (3, 0, -2), (-2, a, 1)} linearly independent ? Let U= span {(1,-2,3), (3,1,5)} Find all t such that (2,1,t) in U −1 Let A = −1 − −1 2 If X R , find the dimension of the solution-space of AX = For what value of m is the set of vectors S = {(-1, 1, 2) , (1,2,-3) , (m, -1, 2)} linearly dependent? Find a basis and dimU if: a U=span{(1,-1,2,0);(-2,1,0,1);(-1,0,0,1); (1,0,1,2)} b U=span{(1,-1,3,0);(5,-2,4,3);(-2,0,7,1)} c U=span{(-1,4,3);(3,0,-2);(-6,2,0)} d U={(a,b,c):a+b+c=0} e U={[a b 0]T: a,b in R} − − 6 , find a basis for the corresponding eigenspaces of A Let A = −1 − 1 −1 3 5 For A = −2 −5 −4 , 1 −1 −1 a find bases of colA and rowA; b find rank(A) Let |u| be the length of vector u and u•v be dot product of two vectors u,v Suppose that |u|=5, |v|=7 and u•v=-3, then what is (3u-v)•(2u+3v)? 10 Which of the following are subspaces of R ? (i) {(0,5a,-17b) |a,b in R} (ii) {(1,a,0) |a in R}` (iii) {(a2,b,3a-5b) |a,b in R} (iv) {(a,b,c) | a/2 - b = 2c; a-b+c=0}