Consider the following function. T: M22 → M₂2 defined by T [W]-[²] y -y Find the following images of the function for vectors A = C₁ ₁ X T(A) + T(B) = T(A + B) = CT(A) = T(CA) = Determine whether T is a linear transformation. O linear transformation not a linear transformation and B = in M₂2 and the scalar c. (Give all answers in terms of a₁, b₁, C₁, ₁, ₂, b₂, C₂ d₂, and c.) .C₂ d₂

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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Consider the following function.
-
T: M22 → M22 defined by
**[**] - [, ², "=²]
y
5
b₁
Find the following images of the function for vectors A =
C₁
X
T(A) + T(B) =
T(A + B) =
CT(A) =
T(CA) =
Determine whether T is a linear transformation.
O linear transformation
O not a linear transformation
and B =
22 b₂
in M22
C₂ d₂.
and the scalar c. (Give all answers in terms of a₁, b₁, C₁, ₁, ₂, b₂, C₂, d₂, and c.)
Transcribed Image Text:Consider the following function. - T: M22 → M22 defined by **[**] - [, ², "=²] y 5 b₁ Find the following images of the function for vectors A = C₁ X T(A) + T(B) = T(A + B) = CT(A) = T(CA) = Determine whether T is a linear transformation. O linear transformation O not a linear transformation and B = 22 b₂ in M22 C₂ d₂. and the scalar c. (Give all answers in terms of a₁, b₁, C₁, ₁, ₂, b₂, C₂, d₂, and c.)
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