Problem 2. Let T : U2x2(R) → U2x2(R) be the linear operator defined on the vector space of 2 x 2 upper triangular matrices as follows: T(A) = [, :]- 1 7 0 8 1 1 0 1 (a) Find the matrix [T]B relative to the basis B = 0 0 (b) Determine whether T is injective and surjective.

Problem 2. Let T : U2x2(R) → U2x2(R) be the linear operator defined on the vector space of 2 x 2 upper triangular matrices as follows: T(A) = [, :]- 1 7 0 8 1 1 0 1 (a) Find the matrix [T]B relative to the basis B = 0 0 (b) Determine whether T is injective and surjective.

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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Concept explainers

Matrices

‘Matrices’ is the plural form of the word matrix, and it is basically a spreadsheet in the form of a box. In mathematics, various functions can be carried out with matrices. Generally, a matrix comes in the shape of a square or rectangle. The elements are distributed horizontally in the form of rows, and vertically in the form of columns.

Question

Problem 2. Let T : U2x2(R) → U2x2(R) be the linear operator defined on the vector space of 2 x 2
upper triangular matrices as follows:
T(A) = [ ]4
1 7
0 8
1
1
0 1
(a) Find the matrix [T]B relative to the basis B =
0 0
0 1
(b) Determine whether T is injective and surjective.
1 2
0 1
6 6
0 0
0 2
0 0
]
(c) Find the transition matrix [IdB.B' where B' =
and B given
as above

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