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You are watching: A linear transformation is a special type of function.

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Transcribed photo text: Determine whether each statement listed below is true or false. Justify each answer. a. A linear transdevelopment is a special type of feature. O A. True. A straight transformation is a role from R" to R" that assigns to each vector x in R" a vector T(x) in R". O B. True. A direct transformation is a role from R to R that asindications to each vector x in R a vector T(x) in R. O C. False. A linear transformation is not a role because it maps even more than one vector x to the exact same vector T(x). OD. False. A linear transdevelopment is not a role bereason it maps one vector x to even more than one vector T(x). b. If A is a 3x5 matrix and also T is a change identified by T(x) = Ax, then the domajor of Tis R$ O A. True. The domain is R3 bereason A has 3 rows, bereason in the product Ax, if A is an mxn matrix then x must be a vector in R". O B. False. The domain is actually R", because in the product Ax, if A is an mxn matrix then x should be a vector in R". O C. True. The doprimary is R bereason A has actually 3 columns, bereason in the product Ax, if A is an mxn matrix then x must be a vector in R". OD. False. The domain is actually R, because in the product Ax, if A is an mxn matrix then x should be a vector in R. c. If A is an mxn matrix, then the selection of the transformation x Axis R". O A. True. The range of the transformation is R", bereason each vector in R™ is a direct combicountry of the rows of A. O B. False. The range of the transdevelopment is R" because the domajor of the transdevelopment is R". OC. False. The array of the transdevelopment is the set of all direct combinations of the columns of A, because each image of the transformation is of the create Ax. OD. True. The array of the transdevelopment is R", because each vector in R™ is a linear combination of the columns of A. d. Eincredibly straight transformation is a matrix transdevelopment. O A. True. Eincredibly linear transformation T(x) deserve to be expressed as a multiplication of a matrix A by a vector x such as Ax. O B. True. Eincredibly direct transdevelopment T(x) can be expressed as a multiplication of a vector A by a matrix x such as Ax. O C. False. A matrix transformation not a linear transformation bereason multiplication of a matrix A by a vector x is not linear. O D. False. A matrix transdevelopment is a distinct direct transformation of the form x Ax wright here A is a matrix e. A transdevelopment T is direct if and just if (C1V1 +2V2) ECT(V1) + C (V2) for all v, and v2 in the domain of T and also for all scalars C, and cz. O O A. False. A transformation T is direct if and also just if T(cu) = CT(u) for all scalars c and also all u in the domajor of T. B. False. A transformation Tis direct if and only if T(u + v) = T(u) + T(v) for all u, v in the doprimary of T. O C. True. This equation properly summarizes the properties vital for a revolution to be linear. D. False.

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A transdevelopment T is straight if and just if T(0) = 0. O