M21001-HW3

M21001-HW3 - MATH 21001 Spring 2010 Homework 3 Hassan...

This preview shows pages 1–3. 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: MATH 21001 - Spring 2010 - Homework 3 Hassan Allouba Problem 1 Determine the general solution for each of the following homogeneous systems. (a) x 1 + 2 x 2 + x 3 + 2 x 4 = 0 , 2 x 1 + 4 x 2 + x 3 + 3 x 4 = 0 , 3 x 1 + 6 x 2 + x 3 + 4 x 4 = 0 . (b) 2 x + y + z = 0 , 4 x + 2 y + z = 0 , 6 x + 3 y + z = 0 , 8 x + 4 y + z = 0 . (c) x 1 + x 2 + 2 x 3 = 0 , 3 x 1 + 3 x 3 + 3 x 4 = 0 , 2 x 1 + x 2 + 3 x 3 + x 4 = 0 , x 1 + 2 x 2 + 3 x 3- x 4 = 0 . (d) 2 x + y + z = 0 , 4 x + 2 y + z = 0 , 6 x + 3 y + z = 0 , 8 x + 5 y + z = 0 . 1 Problem 2 Among all solutions that satisfy the homogeneous system x + 2 y + z = 0 , 2 x + 4 y + z = 0 , x + 2 y- z = 0 , determine those that also satisfy the nonlinear constraint y- xy = 2 z . Problem 3 If A is the coefficient matrix for a homogenous system consisting of four equations in eight unknowns and if there are five free variables, what is rank ( A )? Problem 4 Suppose that A is the coefficient matrix for a homogeneous system of four equations in six unknowns and suppose that...
View Full Document

This note was uploaded on 04/22/2010 for the course MATH 21001 taught by Professor Staff during the Spring '08 term at Kent State.

Page1 / 6

M21001-HW3 - MATH 21001 Spring 2010 Homework 3 Hassan...

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

View Full Document
Ask a homework question - tutors are online