Find the standard matrix for the linear operator T: R3 —) R3 that first transform by the formula T(x,y,z) = (x-y+z,-x+y,y-z), then rotate the resulting vector anti clockwise about the z-axis through an angle θ = 120°, and then project the resulting vector about zx-plane. Hence compute T(1,0,1). 5. Find the standard matrix for the linear operator T:R3 → R3 that first transform by theformula T(x, y, z) = (x- y +z,-x + y, y - z), then rotate the resulting vector anticlockwise about the z-axis through an angle 0 = 120', and then project the resultingvector about zx-plane. Hence compute T(1,0,1).

Given we have given a linear operator T:R3→R3 that transform by the formula T(x, y, z)=(x-y+z,…

5. Find the standard matrix for the linear operator T: R3 → R3 that first transform by the formula T(x, y, z) = (x – y+ z,-x + y,y- z), then rotate the resulting vector anti clockwise about the z-axis through an angle 0 = 120', and then project the resulting vector about zx-plane. Hence compute T(1,0,1). %3D

5. Find the standard matrix for the linear operator T: R3 → R3 that first transform by the formula T(x, y, z) = (x – y+ z,-x + y,y- z), then rotate the resulting vector anti clockwise about the z-axis through an angle 0 = 120', and then project the resulting vector about zx-plane. Hence compute T(1,0,1). %3D

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

Find the standard matrix for the linear operator T: R³ —) R³ that first transform by the formula T(x,y,z) = (x-y+z,-x+y,y-z), then rotate the resulting vector anti clockwise about the z-axis through an angle θ = 120°, and then project the resulting vector about zx-plane. Hence compute T(1,0,1).

5. Find the standard matrix for the linear operator T:R3 → R3 that first transform by the
formula T(x, y, z) = (x- y +z,-x + y, y - z), then rotate the resulting vector anti
clockwise about the z-axis through an angle 0 = 120', and then project the resulting
vector about zx-plane. Hence compute T(1,0,1).

Quantities that have magnitude and direction but not position. Some examples of vectors are velocity, displacement, acceleration, and force. They are sometimes called Euclidean or spatial vectors.

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