Exercise 8.5.5: Consider z²+xz+y = 0 in R³. Find an equation D(x,y) = 0, such that if D(xo, yo) ‡0 and z² + xoz+yo = 0 for some z € R, then for points near (xo, yo) there exist exactly two distinct continuously differentiable functions r₁(x, y) and r2(x, y) such that z = r₁(x, y) and z = r2(x, y) solve z² +xz+y=0. Do you recognize the expression D from algebra?

Exercise 8.5.5: Consider z²+xz+y = 0 in R³. Find an equation D(x,y) = 0, such that if D(xo, yo) ‡0 and z² + xoz+yo = 0 for some z € R, then for points near (xo, yo) there exist exactly two distinct continuously differentiable functions r₁(x, y) and r2(x, y) such that z = r₁(x, y) and z = r2(x, y) solve z² +xz+y=0. Do you recognize the expression D from algebra?

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter4: Eigenvalues And Eigenvectors

Section4.6: Applications And The Perron-frobenius Theorem

Problem 69EQ: Let x=x(t) be a twice-differentiable function and consider the second order differential equation...

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