Show that the (m 1) by (m 1) tridiagonal method matrix A given by ai j = , j = i 1 or j = i + 1, 1 + 2, j = i, 0, otherwise, where > 0, is positive definite and diagonally dominant and has eigenvalues i = 1 + 4 sin i 2m 2 , for each i = 1, 2,... , m 1, with corresponding eigenvectors v(i) , where v(i) j = sin(i j/m).

Lecture 13 Cell Biology Types of intercellular Signaling o Autocrine – cell produces signal and its receptors get the message o Paracrine – cell produces signal and other close by cells’ receptors get the messages o Endocrine – hormones are secreted into the blood stream and travelled over long distances to their target cells. Two...