# Week5 - ECON 117 Mathematical Economics Spring 2008 Week 5...

This preview shows pages 1–4. Sign up to view the full content.

ECON 117 Spring 2008 Mathematical Economics Week 5 Def) Space A that is spanned by ( kn ) < independent n -dimensional vectors has dimension k . We call A is a subspace of . n \ Q) Find the space that is spanned by . 2 2 1 ⎛⎞ =∈ ⎜⎟ ⎝⎠ x \ Q) Find the space that is spanned by ( ) ( ) 3 12 0,1,1 , 1,0,0 == xx \ . Page 1 of 8

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

View Full Document
ECON 117 Spring 2008 Mathematical Economics Def) Vector space V is normed if: , V x a real number for x such that: (i) 0 x and 0 = x iff = x0 (ii) aa ⋅= ⋅ xx where a \ (iii) , V +≤+ xy x y x y ( Note ) Euclidean n-dimensional space is a normed vector space where n \ x is defined such that 22 12 n 2 x =+ + + x " Theorem) Vectors are orthogonal (having a right angle) if , , n xy \ 0 ⋅= where () 1 2 11 1 2 2 ,, nn n y y n x y x y y ⎛⎞ ⎜⎟ ⋅≡ + + + ⎝⎠ "" # x y . Q) . Show that 2 , \ cos θ ′⋅ = x y x y Page 2 of 8
ECON 117 Spring 2008 Mathematical Economics 2. Matrix: Array of vectors 1 2 12 11 12 1 21 () 1 1, , , number of -dim row vectors || | number of -dim column | m n n ij mn mn m im jn m n n m xx x x x × = = ⎡⎤ ⎢⎥ ⎣⎦ = = == −− x

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.

## This note was uploaded on 09/15/2008 for the course ECON 324 taught by Professor Kim during the Spring '08 term at HKUST.

### Page1 / 8

Week5 - ECON 117 Mathematical Economics Spring 2008 Week 5...

This preview shows document pages 1 - 4. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online