MATH 2550 Midterm: MATH 2550 Iowa Exam 3formB
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Suppose a is a 6 5 matrix. If rank of a = 4, then nullity of a : a. If ~x1 and ~x2 are solutions to a~x =~b, then 5~x1 + 8~x2 is also a solution to a~x =~b: a. Is a = diagonalizable: a. yes, b. no, c. none of the above. Suppose a is a square matrix and a~x =~0 has an in nite number of solutions, then given a vector. ~b of the appropriate dimension, a~x =~b has: a. Is a unit vector in the direction of . 0. 6: c. -0. 4, d. -0. 2, e. 0, f. 0. 2, g. 0. 4, h. 0. 6, i. Which of the following is an eigenvalue of (cid:20) 4 4. Suppose a = pdp 1 where d is a diagonal matrix. Suppose also the dii are the diagonal entries of d. if p = [ ~p1 ~p2 ~p3 ] and d11 = d33, then ~p1 + ~p3 is an eigenvector of a: a.
