college level multivariable calculus, vectors + vector calculus (image attached)topic: lagrange multipliers -> system of equations, vector calculus 8. Consider the function f(x, y, z) = x°y+ e9².Use Lagrange multipliers to write out a system of equations to solve for optimizing(a)f subject to the constraint x² + y² = z² + 1. Call this System A. Do NOT attempt tosolve your system.Do the same thing for f subject to the constraint 3x? + 2y? + z? = 1. Call this(b)System B. Again, do NOT attempt to solve your system.(c)case we can guarantee that one of the systems you've written above must have a solution.Which is it and why? Hints: What points are your systems trying to find? What theoremsdo we have related to finding such points?Systems of n equations with n variables don't always have solutions, but in this

Given f(x,y,z)=x3y+eyz We need to find the system of equations to solve for optimizing f subject to…

8. Čonsider the function f (x, y, z) = x°y + e9². (a) f subject to the constraint x2 + y? = z² + 1. Call this System A. Do NOT attempt to solve your system. Use Lagrange multipliers to write out a system of equations to solve for optimizing Do the same thing for f subject to the constraint 3x2 + 2y² + z² = 1. Call this (b) System B. Again, do NOT attempt to solve your system. Systems of n equations with n variables don't always have solutions, but in this case we can guarantee that one of the systems you’ve written above must have a solution. Which is it and why? Hints: What points are your systems trying to find? What theorems do we have related to finding such points?

8. Čonsider the function f (x, y, z) = x°y + e9². (a) f subject to the constraint x2 + y? = z² + 1. Call this System A. Do NOT attempt to solve your system. Use Lagrange multipliers to write out a system of equations to solve for optimizing Do the same thing for f subject to the constraint 3x2 + 2y² + z² = 1. Call this (b) System B. Again, do NOT attempt to solve your system. Systems of n equations with n variables don't always have solutions, but in this case we can guarantee that one of the systems you’ve written above must have a solution. Which is it and why? Hints: What points are your systems trying to find? What theorems do we have related to finding such points?

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter2: Systems Of Linear Equations

Section2.4: Applications

Problem 17EQ

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