MATH 2550 Midterm: MATH 2550 Iowa Exam 3formDans
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Suppose a is a 7 5 matrix. If rank of a = 4, then nullity of a : f. 1. If ~x1 and ~x2 are solutions to a~x =~b, then 5~x1 + 8~x2 is also a solution to a~x =~b: b. 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: e. either no solution or an in nite number of solutions. Then an eigenvalue of a is: e. 0. Suppose a is a 3 4 matrix. Then nul a is a subspace of rk where k : i. Is a unit vector in the direction of . Then if dii are the diagonal entries of d, d11 : e. 0. Which of the following is an eigenvalue of (cid:20) 4 4: g. 2. Suppose a = pdp 1 where d is a diagonal matrix.
