Consider the linear transformation T : R3 → R³ with standard matrix representation: 1 [T]s = -1 0 2 -1 Let {(0, 1,0), (1, 1, 1), (0,0, 1)}. B = (a) Prove that B is a basis for R3. (b) Find the transition matrix Ps.g from the basis B to the standard basis S for R3. (c) Determine the transition matrix PB.S. (d) Determine [T]B. (e) Calculate [T(1, –1, 1)]B.
Consider the linear transformation T : R3 → R³ with standard matrix representation: 1 [T]s = -1 0 2 -1 Let {(0, 1,0), (1, 1, 1), (0,0, 1)}. B = (a) Prove that B is a basis for R3. (b) Find the transition matrix Ps.g from the basis B to the standard basis S for R3. (c) Determine the transition matrix PB.S. (d) Determine [T]B. (e) Calculate [T(1, –1, 1)]B.
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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![Consider the linear transformation T : R³ → R³ with standard matrix representation:
1
[T]s =
-1 0
2
-1
Let
{(0, 1,0), (1, 1, 1), (0,0, 1)}.
B =
(a) Prove that B is a basis for R3.
(b) Find the transition matrix Ps.g from the basis B to the standard basis S for R3.
(c) Determine the transition matrix PB.s.
(d) Determine [T\g.
(e) Calculate [T(1, –1, 1)]B.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F338841ae-abd8-4479-91f2-984147a67a6e%2F24291e33-0c60-4260-a009-4210e1421f6d%2Fv7kfx4x_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Consider the linear transformation T : R³ → R³ with standard matrix representation:
1
[T]s =
-1 0
2
-1
Let
{(0, 1,0), (1, 1, 1), (0,0, 1)}.
B =
(a) Prove that B is a basis for R3.
(b) Find the transition matrix Ps.g from the basis B to the standard basis S for R3.
(c) Determine the transition matrix PB.s.
(d) Determine [T\g.
(e) Calculate [T(1, –1, 1)]B.
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