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Let V1 = R4 and V2 = R2. Let T : V1 → V2 be the...

Let V1 = R4 and V2 = R2. Let T : V1 → V2 be the map dened by T x1 x2 x3 x4 = x1 −x2 + x4 x1 + x2 + x3 + x4 . (a) Show that T is a linear transformation. (b) Let u1 = 1 0 0 −1 , u2 = 0 1 −2 1 .Show that ( u1, u2) is a basis of kerT. (c) Show that imT = V2. (Hint: Compute T(e1) and T(e2)).

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