HW5_Sol - Math 104 Fall 2009 Homework 5 solution set We use...

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

View Full Document Right Arrow Icon
Math 104 Fall 2009 Homework 5: solution set We use the notations below to ease readability. Matrices are bold capital, vectors are bold lowercase and scalars or entries are not bold. For instance, A is a matrix and a ij its ( i,j )th entry. Likewise x is a vector and x j its j th component. The linear span generated by a group of vecotors v 1 , v 2 ,..., v n is denoted by span( v 1 , v 2 ,..., v n ). Problem 1 The equation of a line is y = a + bx . We want to minimize (1 - a ) 2 + ( - 1 - a - b ) 2 + ( - 2 - a - 2 b ) 2 . In matrix form, we need to minimize k c - Az k 2 with A = 1 0 1 1 1 2 , c = 1 - 1 - 2 , z = ± a b ² Solving the equation in the sense of least squares sense gives z = ( A * A ) - 1 A * c = ± 5 6 - 3 2 ² Therefore, the linear equation is y = 5 6 - 3 2 x . Problem 2 Put A = 1 x 1 . . . . . . 1 x n , c = y 1 . . . y n , z = ± a b ² c - Az = y 1 - a - bx 1 . . . y
Background image of page 1

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

View Full DocumentRight Arrow Icon
Image of page 2
This is the end of the preview. Sign up to access the rest of the document.

This document was uploaded on 12/05/2010.

Page1 / 2

HW5_Sol - Math 104 Fall 2009 Homework 5 solution set We use...

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

View Full Document Right Arrow Icon
Ask a homework question - tutors are online