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Unformatted text preview: Practice problems for Midterm 2 1. Suppose that A is a 100 × 100 matrix with all elements equal to zero except for the diagonal elements, a ii = 3. (a) Calculate | A | . (b) Suppose that the matrix B is the same a A , except is has one more nonzero element: b 13 , 74 = 5. Calculate | B | . (c) Suppose that the matrix C is the same a B , except is has one more nonzero element: c 81 , 80 = 7. Calculate | C | . 2. Suppose that the matrix A is given by A = 1 4 3 1 11 16 9 11 2 1 2- 1 10 9- 1 . (a) Does the system AX = 0 have non-zero solutions? Why? (b) How many independent variables does the system AX = 0 have? How many dependent variables? Find all the solutions of the system AX = 0. (c) Suppose we have a non-homogeneous system AX = B , where B = b 1 b 2 b 3 b 4 . Specify the conditions on the components of B which would guarantee that the equation AX = B has non-zero solutions....
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This note was uploaded on 01/12/2010 for the course MATH 421 taught by Professor Nataliakomarova during the Winter '07 term at San Jose State.
- Winter '07