Let A be an n×n n times n real matrix with the property that AT=A. eh to the t , equals eh . Show that if Ax=λx eh x equals lamda x for some nonzero vector x in Cn, blackboard bold cap c to the n , comma then, in fact, λ lamda is real and the real part of x is an eigenvector of A. [Hint: Compute x¯¯TAx, x bar to the t eh x comma and use Exercise 23. Also, examine the real and imaginary parts of A x.]