This preview shows page 1. Sign up to view the full content.
Unformatted text preview: f 1 = 0 i + 2 j + 0 k ; f 2 = 1 i + 0 j + 1 k ; f 3 = 1 i + 1 j + 0 k . Determine iF f 1 , f 2 and f 3 are orthogonal to each other. IF they are not orthogonal to each other, then perForm the Following steps: set u 1 = f 1 ; set u 2 = f 2 proj u 1 f 2 ; set u 3 = f 3 proj u 1 f 3 proj u 2 f 3 . What can you say about the orthogonality oF u 1 , u 2 , and u 3 ? Normalize the vectors u 1 , u 2 , and u 3 and call the results e 1 , e 2 , and e 3 , respectively. (YI: this orthogonalization process is a special case oF the GramSchmidt procedure and it plays an important role in many areas oF applied mathematics.) 4. inally, suppose a 1 = 4, a 2 = 3, and a 3 = 7. Express A in terms oF your new basis vectors e 1 , e 2 , and e 3 . VeriFy that your result is equal to A when written in the standard basis....
View
Full
Document
This note was uploaded on 02/10/2011 for the course APPM 2350 taught by Professor Adamnorris during the Fall '07 term at Colorado.
 Fall '07
 ADAMNORRIS

Click to edit the document details