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The critical points for this optimization problem will thus come from solutions to the following system of equations. 3 = 21x 2 = 4ly 4 = 12\z x² + 2y² + 6z² - 21 = 0 Solve the first equation for 2. 3 = 21x = 3 We will choose to eliminate 1 from 2 = 4ly by substituting this expression for A in order to express x in terms of y and also substitute this expression for A in 4 = 12\z to express x in terms of z. X = y X = (x² , + 2y2 + 6z2 - 21 = 0 Solve the first equation for y in terms of x and the second equation for z in terms of x. Then substitute these two equations into the constraint equation appropriately to get one equation in the variable x. x2 + 2 + 6 - 21 = 0 Ju? - 21 = 0

The critical points for this optimization problem will thus come from solutions to the following system of equations. 3 = 21x 2 = 4ly 4 = 12\z x² + 2y² + 6z² - 21 = 0 Solve the first equation for 2. 3 = 21x = 3 We will choose to eliminate 1 from 2 = 4ly by substituting this expression for A in order to express x in terms of y and also substitute this expression for A in 4 = 12\z to express x in terms of z. X = y X = (x² , + 2y2 + 6z2 - 21 = 0 Solve the first equation for y in terms of x and the second equation for z in terms of x. Then substitute these two equations into the constraint equation appropriately to get one equation in the variable x. x2 + 2 + 6 - 21 = 0 Ju? - 21 = 0

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter2: Systems Of Linear Equations
Section2.2: Direct Methods For Solving Linear Systems
Problem 4CEXP
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The critical points for this optimization problem will thus come from solutions to the following system of equations. 3 = 21x 2 = 4ly 4 = 12\z x² + 2y² + 6z² - 21 = 0 Solve the first equation for 2. 3 = 21x = 3 We will choose to eliminate 1 from 2 = 4ly by substituting this expression for A in order to express x in terms of y and also substitute this expression for A in 4 = 12\z to express x in terms of z. X = y X = (x² , + 2y2 + 6z2 - 21 = 0 Solve the first equation for y in terms of x and the second equation for z in terms of x. Then substitute these two equations into the constraint equation appropriately to get one equation in the variable x. x2 + 2 + 6 - 21 = 0 Ju? - 21 = 0
Transcribed Image Text:The critical points for this optimization problem will thus come from solutions to the following system of equations. 3 = 21x 2 = 4ly 4 = 12\z x² + 2y² + 6z² - 21 = 0 Solve the first equation for 2. 3 = 21x = 3 We will choose to eliminate 1 from 2 = 4ly by substituting this expression for A in order to express x in terms of y and also substitute this expression for A in 4 = 12\z to express x in terms of z. X = y X = (x² , + 2y2 + 6z2 - 21 = 0 Solve the first equation for y in terms of x and the second equation for z in terms of x. Then substitute these two equations into the constraint equation appropriately to get one equation in the variable x. x2 + 2 + 6 - 21 = 0 Ju? - 21 = 0
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