HW 1f 0914

HW 1f 0914 - . If not, give a linear relation between the...

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
MATH 53700 HW 1f 09/14/2011 1. Determine whether or not the set of vectors 1 u = ( 1 1 1 2 , , , - ), 2 u = (1, 1, 3, 0), = 3 u (1, 1 0 1 - - , , ), = 4 u (2, 1, 1, 1) is orthogonal . 2. (a) Let V denote the space of n-tuples of the form ( u , 2 u , 3 u , . .., nu ). Determine whether V is a vector space . (b) Let V denote the space of n-tuples of the form ) , , , ( 2 1 n u u u with addition defined by u + v = ) , , , ( 2 1 n u u u + ) , , , ( 2 1 n v v v ) , , , ( 1 2 1 1 n n v u v u v u - - - Determine whether V is a vector space. 3. Do the vectors v 1 = (1, 0, 1), v 2 = (2, 1 1 - , ), v 3 = (1, 5 2 - , ) span 3 R ? 4. Determine whether the set of vectors u 1 = (2, 3, 0, 0), u 2 = (1, , 5 - 0, 2), u 3 = (3, 1, 2, 2) is linearly independent
Background image of page 1
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: . If not, give a linear relation between the vectors. 5. Determine if u 1 = (1, 1, 1), u 2 = (1, 1-, 2) form a basis for span { v 1 , v 2 } where v 1 = (2, 4, 1), v 2 = (1, 7, 2-) . 6. Obtain an orthonormal set from u 1 = (1, 0, 0), u 2 = (1, 1, 0), u 3 = (1, 1, 1). 7. Given the bases e 1 = (1, 0, 0), e 2 = (1, 1, 0), e 3 = (1, 1, 1), determine the dual vectors * 1 e , * 3 * 2 , e e , then express u = (4 1 5) , ,-, v = (0, 0, 2), w = (5 2 3) , ,-in the dual basis. R.Tam...
View Full Document

Ask a homework question - tutors are online