MATH 251 Final: MATH 304 TAMU Homework FinalPreparation
Document Summary
Math 304 linear algebra sections 505 and 506. The trace of a square matrix is the sum of its diagonal entries. Tr(a) = a11 + a22 + + ann. The trace of a matrix satis es for arbitrary n n matrices a1, a2 and an arbitrary r. Tr(a1 + a2) = tr(a1) + tr(a2), tr( a1) = tr(a1). Let v be the vector space of all real 2 3 matrices. Show that ha, bi := tr(at b). de nes an inner product on v . Let h be the plane in r3 de ned by the equation. Find the point on h that is closest to the point (5, 7, 3). x + 2y + 3z = 0. Let f (x) = x3, g(x) = ex and h(x) = e x , be vectors in the vector space of continuous functions on the real line.
