Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN: 9780470458365
Author: Erwin Kreyszig
Publisher: Wiley, John & Sons, Incorporated
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9. Consider the functions T₁ : M22 → R² and T₂ : R² → M22 satisfying
( [o
d]) = (a, d),
T₁
T₂(1,0) = []
(a) Show that T₁ is a linear transformation.
(b) The function T₂ is a linear transformation. Find T₂(a, b).
(c) Are T₁ T₂ and T₂ o T₁ linear?
(d) Find T₁ T₂(a, b) and T₂0 T₁
O
([d]).
"
T₂(0, 1) =
=
[1
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Transcribed Image Text:9. Consider the functions T₁ : M22 → R² and T₂ : R² → M22 satisfying ( [o d]) = (a, d), T₁ T₂(1,0) = [] (a) Show that T₁ is a linear transformation. (b) The function T₂ is a linear transformation. Find T₂(a, b). (c) Are T₁ T₂ and T₂ o T₁ linear? (d) Find T₁ T₂(a, b) and T₂0 T₁ O ([d]). " T₂(0, 1) = = [1
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