Show that the symmetric rank-one update (2.18) and the BFGS update (2.19) are scale-invariant if the initial Hessian approximations B0 are chosen appropriately. That is, using the notation of the previous exercise, show that if these methods are applied to f (x) starting from x0 Sz0 + s with initial Hessian B0, and to f˜(z) starting from z0 with initial Hessian ST B0S, then all iterates are related by xk Szk + s. (Assume for simplicity that the methods take unit step lengths.)

This problem has been solved! see the answercompute and interpret altman's z-scoresfollowing is selected financial information for ebay, for its fiscal years 2005 and 2006.(in millions, except per share data) 2006 2005current assets $ 4,970.59 $ 3,183.24current liabilities 2,518.39 1,484.93total assets 13,494.01 11,788.99total liabilities 2,589.38 1,741.00shares outstanding 1,368.51 1,404.18retained earnings 4,538.35 2,819.64stock price per share 30.07 43.22sales 5,969.74 4,552.40earnings before interest and taxes 1,439.77 1,445.18compute and interpret altman z-scores for the company for both years. (do not round until your final answer; then round your answers to two decimal places.)2006 z-score = answer2005 z-score = answerwhich of the following best describes the company's likelihood to go bankrupt given the z-score in 2006 compared to 2007.the z-score in 2006 is half of the 2005 score. both z-scores are well above the score that represents a healthy company.the z-score in 2006 is double the 2005 score. the z-score has increased sharply, which suggests the company has greatly increased the risk of bankruptcy.the z-score in 2006 is half of the 2005 score. the z-score has decreased sharply, which suggests the company is in financial distress.the z-score in 2006 is double the 2005 score. the z-score has increased sharply, which suggests the company has greatly lowered the risk of bankruptcy.

Abond purchased for $950 was sold for $980 after one year. the interest received during the year is $25. the bond's yield is:

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