MATH 3000 Midterm: MATH 331 Mizzou Exam 2
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Math 331 quiz 5 solutions: (6 points) let b be a xed 5 2 matrix and let c be a xed 2 4 matrix. Determine whether or not l is a linear transformation. Using rules of matrix multiplication we have: l( a) = b( a)c = bac = l(a), and, l(a1 + a2) = b(a1 + a2)c = ba1c + ba2c = l(a1) + l(a2). Thus l is a linear transformation: (5 points) let l : p3 p2 be de ned by l(p(x)) = xp(2) p(1) (this is a linear transformation you do not need to show this). If p(x) = a + bx + cx2 then l(p(x)) = (a + 2b + 4c)x + (a + b + c). To be in ker(l) we will need a + 2b + 4c = 0 and a + b + c = 0. We end up nding the null space of (cid:20) 1.
