Let \( A \) and \( B \) be \( m \times n \) matrices.(a) Suppose that \( \mathbf{v}^T A \mathbf{w} = \mathbf{v}^T B \mathbf{w} \) for all vectors \( \mathbf{v}, \mathbf{w} \) with real entries. Prove that \( A = B \).

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Answered: Let A and B be m × n matrices. (a)…

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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Let A and B be m × n matrices. (a) Suppose that v"Aw = v"Bw for all vectors v, w with real entries. Prove that %3D