cs3220p3 - Homework 3 1 Basics 1. Find the solutions to the...

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

View Full Document Right Arrow Icon

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

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

Unformatted text preview: Homework 3 1 Basics 1. Find the solutions to the equation 1 2 2 4 x y = 3 6 We notice that the equation x + 2 y = 3 is equivalent to the equation 2 x + 4 y = 6. Hence, all points on the line x + 2 y = 3 are solutions to the above equation, or x y = 1- 1 2 + 3 2 2. Matlab gives me a warning that the matrix A is singular. This is because the matrix we give them is noninvertible and hence we cant solve the linear system of equations uniquely. 2 SPD matrix properties 1. Show that the diagonal elements of A are all positive. Because A is symmetric and positive definite, we know that there exists a triangular matrix B such that A = B T B . Now by definition of A being positive definite, we also know that x T Ax > x 6 = 0. The LHS of this second condition can be expanded using the A = B T B property into x T B T Bx = ( Bx ) T Bx > x 6 = 0. Now consider some B of dimension n n , we know that the diagonal of A = B T B must be a sum of squares of the i th column of B . The following example illustrates the 2...
View Full Document

Page1 / 2

cs3220p3 - Homework 3 1 Basics 1. Find the solutions to the...

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