# prac4 - MAS 3114—Practice Problem Set#4 1 Let vectorx 1...

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: MAS 3114—Practice Problem Set #4 1. Let vectorx 1 = (3 , 5 , 1 , 1) T and vectorx 2 = (- 1 , 1 ,- 1 ,- 1) T , and set W = Span { vectorx 1 ,vectorx 2 } . (a) Compute the distance between vectorx 1 and vectorx 2 . (b) Find an orthonormal basis { vectoru 1 ,vectoru 2 } for W . (c) Let vectorw = (0 , 4 ,- 1 ,- 1) T ∈ W . Express vectorw as a linear combination of vectoru 1 and vectoru 2 . (d) Let vector y = (1 ,- 1 , , 2) T . Find vectors ˆ y ∈ W and vector z ∈ W ⊥ such that vector y = ˆ y + vector z . 2. Short answer questions. If there is not enough information given to answer the question, then say so. (a) Let W = Span { (1 , 2 , 3 , 4) T , (5 , 6 , 7 , 8) T } . Write the equation(s) that the entries of the vector vectorx = ( x 1 ,x 2 ,x 3 ,x 4 ) T ∈ R 4 must satisfy for vectorx to be in W ⊥ . (b) Define what it means for the set { vectorx 1 ,vectorx 2 ,...,vectorx k } ⊂ R n to be orthogonal. (c) What is the orthogonal complement of the null space of A T ? (Possible an- swers: the null space of A , the null space of A T , the row space of A , the column space of A .) (d) Give an orthonormal subset of R 3 which is as large as possible....
View Full Document

{[ snackBarMessage ]}

### Page1 / 4

prac4 - MAS 3114—Practice Problem Set#4 1 Let vectorx 1...

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

View Full Document
Ask a homework question - tutors are online