Using the definitions of the between-class and within-class covariance matrices given by (4.27) and (4.28), respectively, together with (4.34) and (4.36) and the choice of target values described in Section 4.1.5, show that the expression (4.33) that minimizes the sum-of-squares error function can be written in the form (4.37)

An 8-year-old boy named “george” was diagnosed with a rare constellation of five auto-immunediseases; two of these diseases were terminal and could take his life. at the time of diagnosis, thediseases were very aggressive; he faced the possibility of being completely bed-ridden in the next couple of months and facing death within five months. however, george received aggressive treatments and experienced the support of a loving family. after two years of treatments, george began to be angry about his condition. one night, his older brother was goingto bed and he saw his younger brother on the floor. he nudged him and asked, “what are you doing? ” george responded that he was praying because he did not want to be angry at god. he then asked his older brother, “why did god allow these diseases to happen to me? ” the older brother then said, “let’s go and talk to mom and dad.” george approached his parents and posedthis question: “why did god give me all of these diseases? ”the mom and dad come to you and ask, "what should we share with our son? " consider the following questions as you complete your thread: what are the doctrinal issues to consider in this situation? how would these doctrines aid you in sharing with the parents? if the parents requested that you counsel their son, what information would you counsel george?