While practicing computations in MATLAB, you find a 3 x 3 matrix A and vectors v, w with Av = v, Aw = w and v x w + 0. Determine if A could represent: • a projection on a line, • a projection on a plane, • a reflection across a line, • a reflection across a plane, or • a rotation. Justify your answer by providing an example of a matrix and vectors, or a reason why they can't exist.
While practicing computations in MATLAB, you find a 3 x 3 matrix A and vectors v, w with Av = v, Aw = w and v x w + 0. Determine if A could represent: • a projection on a line, • a projection on a plane, • a reflection across a line, • a reflection across a plane, or • a rotation. Justify your answer by providing an example of a matrix and vectors, or a reason why they can't exist.
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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Transcribed Image Text:While practicing computations in MATLAB, you find a 3 x 3 matrix A and vectors v, w with Av = v, Aw = w
and v x w + 0. Determine if A could represent:
• a projection on a line,
• a projection on a plane,
• a reflection across a line,
• a reflection across a plane, or
• a rotation.
Justify your answer by providing an example of a matrix and vectors, or a reason why they can't exist.
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