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2.Find the set of all real numbers x and y such that the endomorphism of R³ represented by the matrix 1 x [0] 1 1 with respect to the basis B in item 2 is a projection.

2.Find the set of all real numbers x and y such that the endomorphism of R³ represented by the matrix 1 x [0] 1 1 with respect to the basis B in item 2 is a projection.

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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I have already answered the first question. I need the answer for the second question that is, to find the set of all real numbers x and y. Thank you.

1. Let F be any field. Show that the transformation that maps (x, y, z) onto (2, -x, y) is an automorphism of F3. Find the matrix representing this automorphism and its inverse with respect to the basis B = {(1,0,0), (0, 1,0), (0,0,1)). 2. Find the set of all real numbers x and y such that the endomorphism of R³ represented by the matrix 1 x y 0x 1 1 x with respect to the basis B in item 2 is a projection.
Transcribed Image Text:1. Let F be any field. Show that the transformation that maps (x, y, z) onto (2, -x, y) is an automorphism of F3. Find the matrix representing this automorphism and its inverse with respect to the basis B = {(1,0,0), (0, 1,0), (0,0,1)). 2. Find the set of all real numbers x and y such that the endomorphism of R³ represented by the matrix 1 x y 0x 1 1 x with respect to the basis B in item 2 is a projection.
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