please include steps Suppose that the three numbers r,, r2, and r3 are distinct. Show that the three functions exp (r,x), exp (r2x), and exp (13x)are linearly independent byshowing that their Wronskian given below is nonzero for all x.111W= exp [(1 +12 +r3) x]•1 2 '3123isIf y1. Y2. . yn are n solutions of the homogeneous nth-order linear equation y" +p, (x)y" "+... + pn- 1(x)y' + P, (x)y = 0 on an open interval I, where eachPicontinuous. Then the Wronskian is W= W(y,. y2:Yn). If y1.1: Y2:Y, are linearly independent, then W#0 at each point of I.---:To simplify W, evaluate the determinant.W= exp [(1 +2 +r3) x] •%3D

Answered: Image /qna-images/answer/a7bc2976-92d0-4cac-824c-5257f97dd3bf.jpg

Suppose that the three numbers r,, 12, and r3 are distinct. Show that the three functions exp (r,x), exp (12x), and exp (r3x) are linearly independent by showing that their Wronskian given below is nonzero for all x. 1 1 1 W= exp [(1 +12+r3)x]* 1 If y1. Y2. y, are n solutions of the homogeneous nth-order linear equation y) + p, (x)y" + Pn - 1(x)y'+P (x)y = 0 on an open interval I, where each p, is continuous. Then the Wronskian is W = W(y,, y2, .., yn). If y,, y2. ... yn are linearly independent, then W#0 at each point of I. To simplify W, evaluate the determinant. W= exp [(1 +12 +r3)*]•O

Suppose that the three numbers r,, 12, and r3 are distinct. Show that the three functions exp (r,x), exp (12x), and exp (r3x) are linearly independent by showing that their Wronskian given below is nonzero for all x. 1 1 1 W= exp [(1 +12+r3)x]* 1 If y1. Y2. y, are n solutions of the homogeneous nth-order linear equation y) + p, (x)y" + Pn - 1(x)y'+P (x)y = 0 on an open interval I, where each p, is continuous. Then the Wronskian is W = W(y,, y2, .., yn). If y,, y2. ... yn are linearly independent, then W#0 at each point of I. To simplify W, evaluate the determinant. W= exp [(1 +12 +r3)*]•O

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter7: Distance And Approximation

Section7.3: Least Squares Approximation

Problem 58EQ

See similar textbooks