a Let T:R" R" be a linear transformation. First let im(T) be defined analogously to the usual image (of a matrix A): Definition m - im(T) = {b R" | T(x) = b for some x ER"}. Now, T is said to be accurate if im(T) = R". 11 True or False: If T is accurate, then n > m. 1.2 True or False: If nm, then T is accurate. Show that if A is a symmetric n x n matrix, with positivel (real) eigenvalues 11,..., An (some of these eigenvalues could be repeated), then A is always happy