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. (²YI: this orthogonalization process is a special case oF the Gram–Schmidt procedure and it plays an important role in many areas oF applied mathematics.) 4. ²inally, 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....
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 Fall '07
 ADAMNORRIS
 Linear Algebra, 1 K, 0 K, 1 j, Standard basis, 0 j

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