A linear transformation is a special type of function. If A is a 3 x 5 matrix and T is a transformation defined by T(x) = Ax, then the domain of T is R³. If A is an m x n matrix, then the range of the transforma- tion x Ax is Rm. Every linear transformation is a matrix transformation. A transformation Tis linear if and only if T(C₁V₁+ C2V2) = C₁T (V₁) + C₂T (v₂) for all v₁ and v2 in the domain of T and for all scalars c₁ and c₂.
A linear transformation is a special type of function. If A is a 3 x 5 matrix and T is a transformation defined by T(x) = Ax, then the domain of T is R³. If A is an m x n matrix, then the range of the transforma- tion x Ax is Rm. Every linear transformation is a matrix transformation. A transformation Tis linear if and only if T(C₁V₁+ C2V2) = C₁T (V₁) + C₂T (v₂) for all v₁ and v2 in the domain of T and for all scalars c₁ and c₂.
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
Ans to 21 please
![each x.
In Exercises 21 and 22, mark each statement True or False. Justify
each answer.
dy
21. a. A linear transformation is a special type of function.
b.
If A is a 3 x 5 matrix and T is a transformation defined
by T(x) = Ax, then the domain of T is R³.
8.00 x 10.00 in
C.
If A is an m x n matrix, then the range of the transforma-
tion x Ax is Rm.
d. Every linear transformation is a matrix transformation.
e. A transformation Tis linear if and only if T(c₁v₁+
C2V2) = C₁T (V₁) + C₂T (v₂) for all v₁ and v2 in the
domain of T and for all scalars c₁ and c₂.
22. a. Every matrix transformation is a linear transformation.
Search
28.
29.
30](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F6147cd51-fae9-4b86-867f-e7a7fe5750a1%2F6e7eda47-0714-47f6-80cc-76ff61bea072%2F94t59hg_processed.jpeg&w=3840&q=75)
Transcribed Image Text:each x.
In Exercises 21 and 22, mark each statement True or False. Justify
each answer.
dy
21. a. A linear transformation is a special type of function.
b.
If A is a 3 x 5 matrix and T is a transformation defined
by T(x) = Ax, then the domain of T is R³.
8.00 x 10.00 in
C.
If A is an m x n matrix, then the range of the transforma-
tion x Ax is Rm.
d. Every linear transformation is a matrix transformation.
e. A transformation Tis linear if and only if T(c₁v₁+
C2V2) = C₁T (V₁) + C₂T (v₂) for all v₁ and v2 in the
domain of T and for all scalars c₁ and c₂.
22. a. Every matrix transformation is a linear transformation.
Search
28.
29.
30
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