\f\fShow that for each j = 1,. .. ,6, the two differential equations (1} and [2) are equivalent under the change of variables (1:) = (if: 1:1?) G) (;)=(f';?;r 31:36:)- Guldanoe. There is no need to work on each of the six cases separately you can deal with all cases simultaneously by shovving that for any numbers r1, {3 , p,q, the above change of variables transforms the equation i u _ cost sint usint u:cost u p d: v _ sint cost cost sint v + q ' into the equation 1 x _ 10: x + p a: y _ ,31 0 l' a ' Then observe that this gives the correct relationship between each pair of matrices A! and B -{t]. .t