1- Suppose 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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Question
Show (Algebraically) that ||Av||=||v|| for all R^2
Also provide a geometric explanation.
Transcribed Image Text:The image shows handwritten mathematical notation. The statement reads:
"Suppose: \( A = \frac{1}{\sqrt{2}} \begin{bmatrix} 1 & -1 \end{bmatrix} \)"
This expression defines a matrix \( A \) which is a \( 1 \times 2 \) matrix or a row vector. The elements of the vector are scaled by the factor \( \frac{1}{\sqrt{2}} \). The entries within the matrix are 1 and -1.
This matrix is often used in linear algebra and signal processing contexts, such as in describing certain orthogonal transformations.
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