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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
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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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
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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