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Prove that the Vandermonde Matrix is invertible if and only if x1,x2,...xm are unique. DO NOT use the formula for the determinant of this matrix, use a different approach that does not involve the determinant of the Vandermonde Matrix.

Prove that the Vandermonde Matrix is invertible if and only if x1,x2,...xm are unique. DO NOT use the formula for the determinant of this matrix, use a different approach that does not involve the determinant of the Vandermonde Matrix.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Prove that the Vandermonde Matrix is invertible if and only if x1,x2,...xm are unique. DO NOT use the formula for the determinant of this matrix, use a different approach that does not involve the determinant of the Vandermonde Matrix. 1x₁x² 1 x ₂ x ² 2 V = 1 x3x² 1 xm x²/ : I IS IS x7- xn-1 n-1 xm
Transcribed Image Text:Prove that the Vandermonde Matrix is invertible if and only if x1,x2,...xm are unique. DO NOT use the formula for the determinant of this matrix, use a different approach that does not involve the determinant of the Vandermonde Matrix. 1x₁x² 1 x ₂ x ² 2 V = 1 x3x² 1 xm x²/ : I IS IS x7- xn-1 n-1 xm
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