For each Linear Operator:S (x, y) = (2x + y, x + 2y)T(x,y,z) = (z,y,x)to determine:(a) The matrix of the operator on the canonical basis;(b) The characteristic polynomial and the eigenvalues.(c) The autospaces and their last bases.(d) An orthonormal space base R3 formed by eigenvectors.(e) The matrix of the operator in relation to the base of item (d).OBS .: For the operator S of the plane, represent in the Cartesian plane the axes defined by the base chosen in item (d).

Note: Since we can solve at most three subparts in a question, we have solved the first three…

For each Linear Operator: S (x, y) = (2x + y, x + 2y) T(x,y,z) = (z,y,x) to determine: (a) The matrix of the operator on the canonical basis; (b) The characteristic polynomial and the eigenvalues. (c) The autospaces and their last bases.

For each Linear Operator: S (x, y) = (2x + y, x + 2y) T(x,y,z) = (z,y,x) to determine: (a) The matrix of the operator on the canonical basis; (b) The characteristic polynomial and the eigenvalues. (c) The autospaces and their last bases.

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

For each Linear Operator:

S (x, y) = (2x + y, x + 2y)

T(x,y,z) = (z,y,x)

to determine:

(a) The matrix of the operator on the canonical basis;

(b) The characteristic polynomial and the eigenvalues.

(d) An orthonormal space base R3 formed by eigenvectors.

(e) The matrix of the operator in relation to the base of item (d).

OBS .: For the operator S of the plane, represent in the Cartesian plane the axes defined by the base chosen in item (d).

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