MATH 310 Midterm: MATH 310 2008 Winter Test 2
Document Summary
Check to ensure that this paper is complete: [15 marks] in the vector space v = p4(r) of polynomials with real coe cients of degree less than or equal to 4, determine whether the following subsets are subspaces. Time: 2 1/2 hours: [15 marks] let v be the 3-dimensional vector space of real-valued functions of the form aex +be2x +ce3x. Show that ex + e2x, e2x + e3x, ex + e3x is another basis, and nd the matrix of t with respect to this second basis: [15 marks] let a be the 3 3 matrix. 1: find the determinant and the trace of a, a has only 2 distinct eigenvalues, one of which equals 1. Find the other eigenvalue of a: show that a is diagonalizable. What is the minimum polynomial of a: [15 marks] let v be the vector space m2 2(r) whose elements are 2 2 real matrices.
