(8 points) Given the linear map T: R 9 R, a) Give the standard matrix...

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(8 points) Given the linear map T: R² 9 → R³, a) Give the standard matrix of T. b) Determine whether T is one-to-one. c) Is the vector X1 [Q]- X2 in the image of T? If so, find d) Is the vector 4 in the image of T? If so, find 9 x1 - 2x2 -x1 + 3x₂ 3x1 - 2x2 X1 X2 A such that T T- X1 21 ([2₂) such that T( = = B 4 9 화 9 (8 points) Given the linear map T: R² 9 → R³, a) Give the standard matrix of T. b) Determine whether T is one-to-one. c) Is the vector X1 [Q]- X2 in the image of T? If so, find d) Is the vector 4 in the image of T? If so, find 9 x1 - 2x2 -x1 + 3x₂ 3x1 - 2x2 X1 X2 A such that T T- X1 21 ([2₂) such that T( = = B 4 9 화 9