1. Determine whcther the function is a lincar transformation or not.a. T: R → R', T(x, y, z)= (r + y,I - y, 2)b. T: R? → R³, T(r, y) = (VT, ry, T)с. Т: М2x2 R, T(A) — а —b — с — d,a bwhcre A:

T:R3→R3T(x,y,z)=(x+y,x-y,z) Let, a,b,c∈R3 and x,y,z∈R3…

Answered: 1. Determine whether the function is a…

Algebra and Trigonometry (6th Edition)

6th Edition

ISBN:9780134463216

Author:Robert F. Blitzer

Publisher:Robert F. Blitzer

ChapterP: Prerequisites: Fundamental Concepts Of Algebra

Section: Chapter Questions

Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...

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]Let ƒ : R → R³ be defined by f(x) = (−5x, 6x, 5x). Is ƒ a linear transformation? a. f(x + y) = -5x-5y, 6x+6y, 5x+5y f(x) + f(y) = -5x, 6x, 5x + -5y,6y, 5y Does f(x + y) = f(x) + f(y) for all x, y E R? Yes, they are equal b. f(cx) = -5cx, 6cx, 5cx c(f(x)) = C -5x, 6x, 5x Does f(cx) = c(f(x)) for all c, x ER? Yes, they are equal c. Is f a linear transformation? f is a linear transformation
Let T: R² →R² be a linear transformation that maps u = O A. O B. O C. O D. 15 -6 -1 - 10 5 ܝ -11 14 -4 -4 into -8 8 and maps v= [2]] into C 13 - 10 Use the fact that T is linear to find the image of 3u + v.
Q.3. Let R, (x) be a reflection of any vector x through the line along the vector u and P, (x) be a projection of any vector x onto the line along the vector u. Find the transformation RP for u =
Suppose T: R2-→R³ is a linear transformation. Let U and V be the vectors given below, and suppose that T(U) and T(V) are as given. Find T(-3U-2V). 14 18 U = V = T(U) = -7 T(V) =-9 3 16 21 T(-3U–2V) = | 0
38. a. Consider a linear transformation T from R³ to R. What are the possible values of dim(ker T)? Explain. b. Consider a linear transformation T from R4 to R'. What are the possible values of dim(imT)? Explain.
Determine whether the function is a linear transformation
Let e1= (1,0) e2=(0,1), x1=(1,6) and x2=(4,−5) Let T: R2→R2 be a linear transformation that sends e1→x1 to and e2→x2. If T maps (−5,−8) to the vector y→, then y = ___

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1. Determine whether the function is a lincar transformation or not. a. T : R → R', T(x,y, z) = (r+ y, -y, 2) %3D b. T: R?R, T(r, y) = (VT, ry, T) c. T: M2x2 R, T(A) = a – b- c- d, [a b whcre A c d