Question: mapping F in the space defined by first projecting onto the plane through the origin with the normal (1,2,5) and then further mapping this

mapping F in the space defined by first projecting onto the plane

mapping F in the space defined by first projecting onto the plane through the origin with the normal (1,2,5) and then further mapping this projected vector with the linear mapping taking the vector (x, y, z) to the vector (2x-3y, 3x+4y+z, xy-z)

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