Find the coordinate matrix of x in Rn relative to the basis B'. B' = {(4, 3, 3), (−11, 0, 11), (0, 9, 2)}, x = (−22, −9, 20)

Write the given second order equation as its equivalent system of first order equations. u" + 5u' + 7u = 0 Use v to represent the "velocity function", i.e. v = Use v and u for the two functions, rather than u(t) and v(t). (The latter confuses webwork. Functions like sin(t) are ok.) u'(t). u' = Now write the system using matrices: u d dt V

Find the matrix A' for T relative to the basis B'. A': = T: R² → R², T(x, y) = (−6x + y, 6x − y), B' = {(1, −1), (-1,5)} -

9. Let and B 3 = {[B]-[-2]} = B' ={[2¹].[6]} be two ordered bases for R². Find the change of basis matrix [I]B'.