MATH 3000 Final: MATH 331 Mizzou Final Exam Solutions
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4(cid:21)(cid:29): let x1 = (1, 1, 0, 1)t , x2 = ( 1, 1, 5, 0)t , and x3 = (1, 4, 1, 3)t . Matrix for l1: l2 rst re ects the vector x in the x-axis, and then rotates the result by 30 counterclockwise. 1 : let v be an inner product space. Suppose that x, y v and x y. Show then that the distance between x and y is (kxk2 + kyk2)1/2: true/false. For each statement determine if it is true or false (true means. If the statement is true then give a brief proof. If the statement is false then give a speci c counterexample: let a and b be similar n n matrices. If a is not invertible then b is not invertible: let x1, x2, and x3 be vectors in r3, considered as an ips using the dot product. Suppose that x1 x2 and x2 x3.
