MATH 1B03 Midterm: MATHEMATICS 1B03 Exam 1 2009 Solutions
Document Summary
Questions 1 6: use the spaces provided. Questions 7 10: complete solutions are expected. Answer: p = q: (6 marks) for the following matrices. 1: (3 marks) (a) write down the inverse of 2 7. 1 (b) write down the transpose of . 1 3 4 (c) write down the 4 4 elementary matrix e such that if ea = b, then b is obtained from a by interchanging the 2nd and 3rd rows of a. Answer true or false. (a) det (at ) = det (a). (b) det (ab) = det (ba). False (c) if a is invertible, then every linear system of the form ax = 0 has a nontrivial solution. False (d) tr (at ) = tr (a). True (e) the adjoint of a square matrix is the transpose of the matrix of cofactors. Note: tr (a) is the trace of a square matrix a.
