MATH-205 Midterm: Bates MATH 205 110912ross205exam
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Name: suppose an economy with three sectors d, w and z has consumption matrix c = . Suppose x, the vector which represents the total number of goods actually produced by the three sectors d, w and z in supplying the nal demands of an open sector is x = . 1a) let d be the nal demand vector of the open sector. 1b) explicitly nd d for the vector x given above. Be smart and take advantage of the many zeros in this matrix. 2b) find the eigenvalues of a, and their multiplicities: suppose the determinant of some 4x4 matrix m is 3. Next to each of the following matrices, write its determinant. 4a) it"s a fact that = 5 is an eigenvalue of m . Find m v. then determine if the result says that v is an eigenvector of m . 4d) use your calculator to nd p 1. Name: suppose that a = p.
