Question: 1. Define a linear transformation T : RS - R3 by the formula T(x, y, z) = (3x + 2, - 2x + 2y +

1. Define a linear transformation T : RS - R3 by the formula T(x, y, z) = (3x + 2, - 2x + 2y + z, -2y - 2z), and let V be the plane x + 2y + 3z = 0. (a) Find det(T). (b) Show that V is stable under T (in other words, show that if v E V then I (v ) EV ). (c) Find det(Tv ), where Tv is the restriction of T to V. Are det (T) and det(Tv) equal

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