In line to the standard basis for R³, the matrix of the linear operator T:R³ R³ is -3 -2 -2 A= 0 1 0 4 2 3 a. Give a formula for T(x,y,z). b. Show that T is an isomorphism and find a formula for T-¹(x,y,z). c. With respect to the basis B = {(1, -1, -1), (1, 0, 2), (1,0, -1)} for R³ find the matrix of T relative to B.

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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Sample Problem: Show all necessary solution.
In line to the standard basis for R³, the matrix of the linear operator
T:R³
R³ is
-3 -2 -2
A= 0 1 0
4
2 3
a. Give a formula for T(x,y,z).
b. Show that T is an isomorphism and find a formula for T-¹(x,y,z).
c. With respect to the basis B = {(1, -1, -1), (1, 0, 2), (1,0, -1)} for R³
find the matrix of T relative to B.
Transcribed Image Text:Sample Problem: Show all necessary solution. In line to the standard basis for R³, the matrix of the linear operator T:R³ R³ is -3 -2 -2 A= 0 1 0 4 2 3 a. Give a formula for T(x,y,z). b. Show that T is an isomorphism and find a formula for T-¹(x,y,z). c. With respect to the basis B = {(1, -1, -1), (1, 0, 2), (1,0, -1)} for R³ find the matrix of T relative to B.
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