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
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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).

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