Please provide a proof that the trace of the product of two matrices i.docx

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Please provide a proof that the trace of the product of two matrices is independent of the order of the factors. i.e. TR(AB) = TR (BA) I am trying to prove that TR (AAtranspose) = TR (AtransposeA), (have the same non zero eigenvalues). Thanks Solution Let A=(a ij ) and B=(b ij ) with i>=1, j<= n. Moreover, let AB = (c ij ) and BA = (d ij ) Then, tr(AB) = sum(i=1 to n) c ii = sum(i=1 to n) sum(j=1 to n) a_ ij b_ ji = sum(j=1 to n) sum(i=1 to n) b ji a ij = sum(j=1 to n) d_ jj = tr(BA). .

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Prepare the financial ratios for J.C. Penney Company, Inc. (JCP) for the years indicated below. Use the JCP financial documents (Balance Sheets and Income Statements) for Calendar Years 2011, 2012, 2013 to calculate the required Financial Ratios and reference in your assessment analysis. Including the following: Prepare the financial ratios for 2011, 2012, 2013. Comment on the differences between J.C. Penney\'s ratios and the industry averages. Determine the trends evident in the financial statements. Write a 3-page memo divided into the following sections: Liquidity. Asset management. Long-term debt-paying ability. Profitability. I have the documents that were given to me (balance sheet and income statement) but I dont know how to attach them for your review. These are made up numbers not the real statements online. Solution Take a snap and attach the image. .

Prepare the financial ratios for J-C- Penney Company- Inc- (JCP) for t.docx

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Please name the following net ionic c THAT HAVE AN ARROW NEXT TO THEM 4. Naming Ionic Compounds Write the correct name for each of the following ionic compounds Formula Name Nslac0 2 Pb(HCO) 3. Al:S uummum Sulud ? 10. Na CrO Sadumshromate Potnssiun Chroanat 12. ?CuP 13. MgiN 15 NH MnO 17 BaSO 8. SnlNO, 19. AgCIO 20. Cu(HSO;2 um Sullate Silver chiias Solution 2) Pb(HCO3)2 ----------------> lead bicarbonate 6) CoF3 ----------------> cobalt (III) fluoride 7) Fe2(HPO4)3----------------> Iron (III) monohydrogen phosphate 9) SnO2 -------------------->Tin (IV) oxide 12) Cu3P --------------------> copper(I)phosphide 15) NH4 MnO4 ------------------------> ammonium permanganate .

Please name the following net ionic c THAT HAVE AN ARROW NEXT TO THEM.docx

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Preparation of cyclohexene from cyclohexanol Preparation of cyclohex.docx

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Potassiumiodide(KI)exhibitspredominantly ionic bonding- The K-- and I-.docx

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Polyvinyl alcohol (PVA) is generally obtained by hydrolysis from polyvinyl acetate, The solubility of PVA in water is increased up to 87% of the extent of hydrolysis but the solubility is rather reduced It is showing, Explain why Solution This may be due to the hydrogen bonding interactions. In the case of fully hydrolysed polyvinyl alcohols, the inner molecuar hydrogen bonding will be very high.That causes insolubility. But in the case of partially hydrolysed polyvinyl alcohols,the hydrogen bonding is balancing with with the desired aqueous solubility. The residual acetate groups reduce the combination by reducing the regularity of the chain structure. Hence the answer. .

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Please provide a proof that the trace of the product of two matrices i.docx

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Please provide a proof that the trace of the product of two matrices i.docx