Let A be an n n matrix with distinct real eigenvalues 1, 2, . . . , n. Let be a scalar that is not an eigenvalue of A and let B = (A I ) 1. Show that (a) the scalars j = 1/(j ), j = 1, . . . , n are the eigenvalues of B. (b) if xj is an eigenvector of B belonging to j , then xj is an eigenvector of A belonging to j . (c) if the power method is applied to B, then the sequence of vectors will converge to an eigenvector of A belonging to the eigenvalue that is closest to . [The convergence will be rapid if is much closer to one i than to any of the others. This method of computing eigenvectors by using powers of (A I ) 1 is called the inverse power method.]

EnergyandMetabolism 10.24.16 • Whatrequiresenergyinanorganism o Creatingmacromolecules o Transportingsolutesinandoutofcells • Energy:thecapacitytodowork o Kineticenergy:motion o Potentialenergy:storedenergy o Chemicalenergyistheamountofpotentialenergystoredinthe chemicalbonds....