MATH-205 Midterm: Bates MATH 205 121311buell205exam
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Using a and ~b above, write the associated system of linear equations described by the matrix equation a~x = ~b: (3 pts) Using a and ~b above, write the associated system vector equation described by the matrix equation a~x = ~b: (4 pts) If so, nd a basis for the eigenspace for = 1. What is the characteristic equation of a? (hint: you shouldn"t have to do any calculation. : (3 pts) Find p and d such that a = p dp 1): (4 pts) Give a good explanation: (13 points) determine which of the following are subspaces of the appropriate vectorspaces. If the set is a subspace, then nd a basis and state the dimension of the subspace. If not, explain why: (4 pts, (4 pts) w = {all 2 2 invertible matrices } W ={polynomials of the form a + bt2, where a, b r}: (5 pts) W = r + t + u s + t u.
