The matrices A₁ A3 = = 1 :] A₂ 9 00 = 0 1 [83] 00 0 0 0 0 [8], 4 = [8] 1 0 1 18888 9 form a basis for the linear space V = R2×2. Write the matrix of the linear transformation T: R²×2 → R²×2 such that T(A) = 15A + 14AT relative to this basis.

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter9: Systems Of Equations And Inequalities
Section9.8: Determinants
Problem 8E
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The matrices
A₁
A3
=
=
1
:] A₂
"
00
=
0
1
[83]
00
0 0
0 0
[18], 4 = [8]
A4
0
1
18888
"
form a basis for the linear space V = R2×2. Write the matrix of the linear
transformation T: R²×2 → R²×2 such that T(A) = 15A + 14AT relative to
this basis.
Transcribed Image Text:The matrices A₁ A3 = = 1 :] A₂ " 00 = 0 1 [83] 00 0 0 0 0 [18], 4 = [8] A4 0 1 18888 " form a basis for the linear space V = R2×2. Write the matrix of the linear transformation T: R²×2 → R²×2 such that T(A) = 15A + 14AT relative to this basis.
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