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

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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...
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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.

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

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