Question: Let P: V R and Q : V R be linear trans-formations, where V is a vector space. Define T: V R2

Let P: V → R and Q : V → R be linear trans-formations, where V is a vector space. Define T: V → R2 by T(v) = (P(v), (Q(v)).
(a) Show that T is a linear transformation.
(b) Show that ker T = ker P ∩ ker Q, the set of vectors in both ker P and ker Q.

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