NullSpaceExample-2003

NullSpaceExample-2003 - AEB 6533 Some Examples of...

Info iconThis preview shows pages 1–3. Sign up to view the full content.

View Full Document Right Arrow Icon
AEB 6533 Some Examples of Nullspaces I. Starting with a simple 2*3 example, assume that we have the matrix equation 1 2 3 11 1 5 011 6 x Ax b x x   =⇒ =  A. Note that by row operations the A matrix can be transformed to 111 11 102 01 0 1 1 = B. This expression implies the following homogeneous relationships: 13 23 20 0 xx + = + = 1. Setting 3 1 x = yields 1 2 2 1 x x = − = − 2. Or in vector form: 2 1 1 z = C. Next we confirm that z is the nullspace. We do this by confirming that both vectors of the A matrix are orthogonal to the nullspace: () 2 2 1 1 0 1 2 011 1 0110 1 −= −++= −=−+= D. Implications of the nullspace: 1. Start by defining a feasible solution: 51 1 1 1 1 5 1 0 2 1 1 60 1 0 1 1 6 0 1 1 6 11 1 1 1 6 0 5 6 6 0 Ax     =         −− + ⇒= = + 2. Next, we would like to generate another feasible point based on this solution and the nullspace matrix:
Background image of page 1

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

View Full DocumentRight Arrow Icon
AEB 6533 – Static and Dynamic Optimization Nullspace Examples Professor Charles B. Moss 2 () 1 * 2 3 11 2 61 01 x x xZ p x p x     =+ = +
Background image of page 2
Image of page 3
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 11/08/2011 for the course AEB 6533 taught by Professor Moss during the Fall '08 term at University of Florida.

Page1 / 4

NullSpaceExample-2003 - AEB 6533 Some Examples of...

This preview shows document pages 1 - 3. Sign up to view the full document.

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