III) Suppose that the linear map T : R - R' satisfies00 00 0-0-0-0(0)2What are det T and trace T?IV) Let T : R → R be the linear map defined byT(11, 12, 13, 14) = (x2 – *3, 2x1- 5x, - 5x3 2a4,-2x1 + 4x, + 6x, + 2a,).Give the matrix of the dual map T': (R')' → (R*)' in the dual bases of the standardbases of R' and R'. I) If W is the span in R of the following 4 vectors0 0 0 04.what is the dimension of its annihilator (W)°?II) If A E Mat3x3, for which one of these values of A is det A 0.a) A =0.1 00.b) A = | 211c) A =-11111III) Suppose that the linear map T: R'→ R' satisfies000000009.T.What are det T and trace T?IV) Let T: R!> R' be the linear map defined by

Given :- Suppose that the linear map T : ℝ4 → ℝ4 satisfies T 1000 = 2622 , T 0100 = 1311 , T 0010…

Answered: III) Suppose that the linear map T:…

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III) Suppose that the linear map T: R-R' satisfies 00 0-0-0-0-0-0 2 2. What are det T and trace T?

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

III) Suppose that the linear map T : R - R' satisfies
00 00 0-0-0-0
(0)
2
What are det T and trace T?
IV) Let T : R → R be the linear map defined by
T(11, 12, 13, 14) = (x2 – *3, 2x1- 5x, - 5x3 2a4,-2x1 + 4x, + 6x, + 2a,).
Give the matrix of the dual map T': (R')' → (R*)' in the dual bases of the standard
bases of R' and R'.

I) If W is the span in R of the following 4 vectors
0 0 0 0
4.
what is the dimension of its annihilator (W)°?
II) If A E Mat3x3, for which one of these values of A is det A 0.
a) A =
0.
1 0
0.
b) A = | 2
1
1
c) A =
-1
1
1
1
1
III) Suppose that the linear map T: R'→ R' satisfies
00000000
9.
T.
What are det T and trace T?
IV) Let T: R!
> R' be the linear map defined by

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