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- A translation in R2 is a function of the form T(x,y)=(xh,yk), where at least one of the constants h and k is nonzero. (a) Show that a translation in R2 is not a linear transformation. (b) For the translation T(x,y)=(x2,y+1), determine the images of (0,0,),(2,1), and (5,4). (c) Show that a translation in R2 has no fixed points.Find a basis B for R3 such that the matrix for the linear transformation T:R3R3, T(x,y,z)=(2x2z,2y2z,3x3z), relative to B is diagonal.IfT: R³ R³ is a linear transformation such that -(:D)- then T = 3 *(C)-[E]· ·(C)-··(CD) - CH = -3 T = 4 T 7 T
- Find the inverse of the linear transformation x1 = x2 = x3 = Y1+ Y₁+ Y1+ Y1 Y2 Y3 = = = 4x1 5x1 x1 -8x2 -29x3 -11x2 -38x3 - 2x2 -7x3 Y2+ Y2+ Y2+ Y3, Y3₁ Y3.Show that the transformation T defined by T(x1, X2) = (2x,- 3x,, x1 +4, 5x,) is not linear. %3DDoes this equation define a linear transformation from R3 to R2?