Let T: IR2 > R2 reflection (or orthogonal symmetry) with respect to the line 2x - y = 0. We call back that the vector a-(-) is orthogonal to the line in question and the vector b = (;) is on this line, a) Give T (a) and T (b) (think about the geometry of reflection) b) Give the canonical matrix of T. Hint: use a) and an inverse matrix and a c) Express the vector e = (6) as a linear combination of a and b and using linearity of T, give T (e1). Do the same with e- () d) Using c), find the canonical matrix of T and give the vector obtained by the reflection of the vector (3) in relation to the line in question.

Let T: IR2 > R2 reflection (or orthogonal symmetry) with respect to the line 2x - y = 0. We call back that the vector a-(-) is orthogonal to the line in question and the vector b = (;) is on this line, a) Give T (a) and T (b) (think about the geometry of reflection) b) Give the canonical matrix of T. Hint: use a) and an inverse matrix and a c) Express the vector e = (6) as a linear combination of a and b and using linearity of T, give T (e1). Do the same with e- () d) Using c), find the canonical matrix of T and give the vector obtained by the reflection of the vector (3) in relation to the line in question.

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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