This preview shows page 1. Sign up to view the full content.
Unformatted text preview: nal.
2 2 2 T rue. W e have u v u 2u v v u v , so u v 0 and u and v
are orthogonal.
2 2 2 2 2 d. F or an m n m atrix A and 1 i m , if x in the null space o f A then x is
orthogonal t o A i . , the i th r ow of A .
T rue. If x in the null space of A then A x 0 but the i th c omponent of A x is
A i . x , w hich is zero.
n 6 . V erify the parallelogram law for v ectors u and v in : u v u v 2 u 2 v .
2 2 2 2 W e have u v u v u 2u v v u 2u v v 2 u 2 v .
2 7 . G iven v ectors u and v in 2 n 2 2 2 2 2 2 , consider vectors of the form v u, for all scalars . a. D etermine so that v u is orthogonal...
View Full
Document
 Spring '08
 PAVLOVIC
 Matrices, Formulas

Click to edit the document details