{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

A4_soln

# A4_soln - Math 235 Assignment 4 Solutions 1 Determine which...

This preview shows pages 1–2. Sign up to view the full content.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Math 235 Assignment 4 Solutions 1. Determine which sets of vectors are orthonormal in R 3 under the standard inner product. If a set is only orthogonal, normalize the vectors to produce an orthonormal set. a) 1 / 2 2 / 3 , - 4 3 . Solution: We have ( 1 2 , 2 3 , 0) · (- 4 , 3 , 0) =- 2 + 2 + 0 = 0. Hence, they are orthogonal. We have k ( 1 2 , 2 3 , 0) k = q 1 4 + 4 9 + 0 = q 25 36 = 5 6 and k (- 4 , 3 , 0) k = √ 16 + 9 + 0 = 5. Hence, an orthonormal set is 3 / 5 4 / 5 , - 4 / 5 3 / 5 b) 1 / √ 3 1 / √ 3 1 / √ 3 , 1 / √ 6 1 / √ 6- 2 / √ 6 , 1 / √ 2 1 / √ 2 . Solution: Observe that ( 1 √ 2 , 1 √ 2 , 0) · ( 1 √ 6 , 1 √ 6 ,- 2 √ 6 ) = 1 √ 3 , hence the set is not even orthogonal. 2. Determine which sets of vectors are orthonormal in M (2 , 2) under the inner product < A, B > = tr( A T B ). If a set is only orthogonal, normalize the vectors to produce an)....
View Full Document

{[ snackBarMessage ]}

### Page1 / 3

A4_soln - Math 235 Assignment 4 Solutions 1 Determine which...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online