MATH 1B03 Midterm: MATHEMATICS 1B03 Exam 1 2009
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Questions 1 6: use the spaces provided. Questions 7 10: complete solutions are expected. 1: (3 marks) (a) write down the inverse of 2 7. 1 4 : (b) write down the transpose of . 0 1 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. Note: tr (a) is the trace of a square matrix a. 2: (2 marks) write down the system of linear equations of which. Note: put your answers in the boxes provided ( none is a possible answer ). Also show your work for this question as well as for questions. 8, 9, and 10: (4 marks) by computing the adjoint, nd the inverse of. 5 8: (4 marks) find the eigenvalues and eigenvectors for the matrix.
