1. The function T: R R is defined as follows 0 -2 -1 2 1 T(v)...

 

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1. The function T: R R is defined as follows 0 -2 -1 2 1 T(v) = Av = V -2 0 4 (a) Show that T is a linear transformation from R to R'. (b) Find the kernel of T. (c) Find a basis for the range of T. 2. (a) Determine whether the set is linearly independent or linearly dependent, explaining your answer. (i) S = {(1,-2), (-3,6)}. (ii) S = {(1,2, 0), (-3,0, 1), (0, 2, 2)}. %3D (b) Find the eigenvalues and the corresponding eigenvectors of 0. A 2 1. The function T: R R is defined as follows 0 -2 -1 2 1 T(v) = Av = V -2 0 4 (a) Show that T is a linear transformation from R to R'. (b) Find the kernel of T. (c) Find a basis for the range of T. 2. (a) Determine whether the set is linearly independent or linearly dependent, explaining your answer. (i) S = {(1,-2), (-3,6)}. (ii) S = {(1,2, 0), (-3,0, 1), (0, 2, 2)}. %3D (b) Find the eigenvalues and the corresponding eigenvectors of 0. A 2

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The function TR is de fined as follows Tv ... View the full answer