4 1.Recall the Vandermonde matrix X given in (3.1.3), and define1..V.(x)det1%3|Xn-1 x-11x2..(а)Show that V„(x) is a polynomial of degree n, and that its roots areXo,..., x,n-1: Obtain the formulaV,(x) = (x - x,) · . (xx,-1)Vn-1(×n-1)...Hint: Expand the last row of V,(x) by minors to show that V,(x) is apołynomial of degree n and to find the coefficient of the term x".(b)Showdet ( X) = V,(xn) =п («,- х,)0

As per the question we have to prove the given recurrence relation of the nth order Vandermonde…

Recall the Vandermonde matrix X given in (3.1.3), and define 1 V,(x) det 1 %3D Xn-1 Xn-1 n-1 1 Show that V,(x) is a polynomial of degree n, and that its roots are Xo, ..., x,–1. Obtain the formula V„(x) = (x - x) (x - x,n-1)Vn-1(×n-1) Hint: Expand the last row of V„(x) by minors to show that V„(x) is a połynomial of degree n and to find the coefficient of the term x". Show det ( X) = V„(x„) II 0sj

Recall the Vandermonde matrix X given in (3.1.3), and define 1 V,(x) det 1 %3D Xn-1 Xn-1 n-1 1 Show that V,(x) is a polynomial of degree n, and that its roots are Xo, ..., x,–1. Obtain the formula V„(x) = (x - x) (x - x,n-1)Vn-1(×n-1) Hint: Expand the last row of V„(x) by minors to show that V„(x) is a połynomial of degree n and to find the coefficient of the term x". Show det ( X) = V„(x„) II 0sj

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 70EQ

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