find bases of colA and rowA; b.. Let |u| be the length of vector u and u•v be dot product of two vectors u,v.
Trang 11 Find m for which (1,-3,m) lies in the subspace spanned by (1,-1,0) and (5,-3,1)
2 For what value of a is the set of vectors S = {(-1, 2, 5), (3, 0, -2), (-2, a, 1)}
linearly independent ?
3 Let U= span {(1,-2,3), (3,1,5)} Find all t such that (2,1,t) in U
4 Let
A
−
XR , find the dimension of the solution-space of AX = 0
5 For what value of m is the set of vectors S = {(-1, 1, 2) , (1,2,-3) , (m, -1, 2)} linearly dependent?
6 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}
7
Let
A
, find a basis for the corresponding eigenspaces of A
8 For
A
−
,
a find bases of colA and rowA;
b find rank(A)
9 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 3
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}.