Let V be a Vectorspace over field F spanned by a finite set fo vectors.docx

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Let V be a Vectorspace over field F spanned by a finite set fo vectors v1,v2,....,vm.Then any Lineraly Independent subset of V is finite and contains a maximum of m elements Solution Let S be any arbitrary subset of V with n elements wi. We need to show that n<=m Enough to Show: S is LD over F such that ai belongs to F where all ai\'s not 0 and Summation of ai*wi = 0 Now as wi belongs to F,we can write wi = summation(aji*vj) Now,there exists n elements xi such that Summation(xi*wn) = 0 Substituting wi value in this equation we get Double Summation((xi*aji)*vj) = 0 It has m equations and n unknowns To solve we need no. of equations >= no. of variables hence n<=m .

Let V be a Vectorspace over field F spanned by a finite set fo vectors v1,v2,....,vm.Then any
Lineraly Independent subset of V is finite and contains a maximum of m elements
Solution
Let S be any arbitrary subset of V with n elements wi.
We need to show that n<=m
Enough to Show: S is LD over F such that ai belongs to F where all ai's not 0 and Summation of
ai*wi = 0
Now as wi belongs to F,we can write wi = summation(aji*vj)
Now,there exists n elements xi such that Summation(xi*wn) = 0
Substituting wi value in this equation we get
Double Summation((xi*aji)*vj) = 0
It has m equations and n unknowns
To solve we need no. of equations >= no. of variables
hence n<=m

Let V be a Vectorspace over field F spanned by a finite set fo vectors.docx

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Let F <= L be a finite extension of fields, and let L = F[a] for some a in L, Show that |F(L/F)| < infinity. where F(L/F) is the set of intermediate fields between F and L Solution given. F<=L so, F/L <= 1 L/F >=1 given L= F(a) hence F(a)/ F >=1 F (L/F) = F ( F(a)/F)) but F(a)/ F >=1 hence it is limited to 1 and greter than that so that we confidently say that it is less than infinite .

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Many intuitively plausible beliefs conflict with science. For example, the belief that the Sun moves around a stationary Earth conflicts with current astronomy. Give at least one other intuitively plausible belief that conflict with either Copernican astronomy or Newtonian physics or both and discuss why it is anomolous. Solution It was earlier believed that the universe was static, i.e. it neither contracts nor expands. But it was found by Hubble that the objects which were farther away were moving more quickly away than the nearby ones. Recently, in 1999 it was found that universe was expanding and this expansion is accelerating. .

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maom an learning What is the concentration of an HBr solution if 28.5 mL of a 0.200 M NaOH solution are needed to titrate 55.5 mL of the acid? Number Solution Before dilution After dilution M1 = 0.2M M2 = V1 = 28.5ml V2 = 55.5ml M1V1 = M2V2 M2 = M1V1/V2 = 0.2*28.5/55.5 = 0.1027M final concentration = 0.1027M .

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Let be unknown constants and consider the linear system: This system has a unique solution whenever . h does not equal ____? If is the (correct) value entered above, then the above system will be consistent for how many value(s) of ? A. a unique value B. infinitely many values C. no values Solution the system will have a unique solution when the determinant of the coefficient matrix ? 0 So according to me A is correct option .

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made a year end adjusting entry to accrue interest on a note payable that has the interest rate stated separately from the principal amount made a year end adjusting entry to accrue interest on a note payable that has the interest rate stated separately from the principal amount Solution Answer: Year end adjusting entry for Accrued interest: Interest Expense Debit Interest payable Credit (Being interest on notes accrued) .

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List some advantages of having a well developed international code of ethics that would guide international marketing and operations of a company? Conversely, what are some disadvantages that you can think of? Solution advantages-it forces a large number of people in the firm to think through, in a fresh way, their mission and the important obligations they as a group and as individuals have to the firm, to each other, to their clients and customers, and to society as a whole. Second, once adopted a code can be used to generate continuing discussion and possible modification to the code. Third, it could help to inculcate in new employees at all levels the perspective of responsibility, the need to think in moral terms about their actions, and the importance of developing the virtues appropriate to their position. disadvantages-inequality in basic social goods such as income and wealth distribution. .

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List several of the major differences between manufacturing and service operations and then articulate the importance of a strong manufacturing base to the overall economy. Solution Manufacturing starts from desingning a part and producing it. So it includes all the things such as Raw material, R and D , logistics. Service operaion does not provide any tangible objects . They are basicaly doing service such as Barber, police etc The importance of strong manufacturing is that the country is self sufficient in manufacturing the products and technology is highly developed. This decreases the imports and increases the export which is good for economy .

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Mack and Joan are married but Mack moved out of the family home in October 2014. They have two children, May, age 9, and Milt, age 3. Mack and Joan together paid more than half of the support for the children and the children lived with Joan all year. There is no legal separation or written agreement that states who is entitled to the children Solution The correct answer is: C.Mack and Joan must file married filing separately since they cannot agree to file married filing jointly. The children are qualifying children for both parents so they need to agree on how to claim the children. They can each take one of the children as a dependent and the child tax credit and /or the additional child tax credit or they can agree for one parent to claim both children .

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luonbcator assignment-take uonor ior SPeCIes war acuAS OUTIOS ouy acceptor for species that act as acceptors only both for species that act as both donors and acceptors neither for species that act neither as donors nor as acceptors. H3C Si 2req CH3 Hydrogen bonding behavior 2req NH Hydrogen bonding behavior both Hydrogen bonding behavior CH3 CH3 Hydrogen bonding behavior acceptor Solution Hydrogen bond donor is the atom (H) attached to more electronegative atoms like F, O and N. While acceptor is the one which has more electronegativity with lone pair of electrons on hetero atoms like F, N and O etc. 1. Neither, since it don\'t have Hydrogen and lone pair of electrons on hetero atom Si. 2. Both, donor and acceptor 3. Acceptor only since lack of hydrogen on oxygen 4. Acceptor onlt .

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Luther recently received $30,000 of compensation for some consulting work (paid in cash). David recently received $30,000 of interest income from City of Ft. Lauderdale bonds. Both taxpayers report no taxable income from these transactions. Is this considered tax avoidance or tax evasion? What is the difference, if any, between the two? Solution Both of these are Tax evasion. Reason - The income is reportable to the IRS and the taxpayers are not reporting it. This is illegal and tax evasion. Difference between tax evasion and tax avoidance Tax Avoidance - This is legal. It is simply minimizing your taxable income by taking all deductins and using legal avenues to avoid paying taxes using legitimate tools and deduction methods. Tax Evasion - This is illegal. It involves not paying taxes that you owe. Tax Evasion involves tax payers who deliberately are not reporting income or over stating their deductions. .

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LS P Explain how one can be certain whether an unknown contains the I ion or the Br ion. Include appropriate equation(s). 3. how you could distinguish chemically between the following pairs of sub- stances (in separate test tubes) in one or two steps. In each case, tell what yo would observe. Include equations for reactions occurring. 4. Tell a) NaCl and NaNO, solutions Solution 3. Identification of anion Add AgNO3 solution AgNO3(aq) + I-(aq) ---> AgI(deep yellow precipitate) + NO3-(aq) and, AgNO3(aq) + Br-(aq) ---> AgI(pale yellow precipitate) + NO3-(aq) So adding AgNO3 gives two different color precipitate with I- and Br- and thus ions can be confirmed. 4. Difference between pairs a) NaCl and NaNO3 solution Add AgNO3 solution to them. NaCl formed white precipitate of AgCl. NaNO3 does not form any such precipitate. .

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List three qualities of software that make it vulnerable Solution The three qualities of the software which make it vulnerable are : 1 .Process : processes utilize some data like metrics, test results etc to check whether the security needs are met or exceed the policy compliance 2.Metrics :These metrics are used to provide some bench mark or base line for the measurment of the application security. 3.Testing Activities :Test the application software which is been developed. It includes cross-site scripting tests etc. these activities identify any vulnerabilities injected inside the software. If any of the above qualities are not met with the standards will make the software vulnerable. .

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List and define the factors that are important to successful implementation effort. Solution Several factors are important to the successful implementation of a system, including management support, the involvement of users, and user expectations. Additionally, commitment to the project, commitment to change, and extent of project definition and planning are important: Commitment to the project refers to managing the project so that the problem being solved is well understood and the target system actually solves the problem. Commitment to change means being willing to change behaviors and procedures. The premise of project definition and planning is that more extensive planning is more effective than less extensive planning. .

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1. Let V be a Vectorspace over field F spanned by a finite set fo vectors v1,v2,....,vm.Then any Lineraly Independent subset of V is finite and contains a maximum of m elements Solution Let S be any arbitrary subset of V with n elements wi. We need to show that n<=m Enough to Show: S is LD over F such that ai belongs to F where all ai's not 0 and Summation of ai*wi = 0 Now as wi belongs to F,we can write wi = summation(aji*vj) Now,there exists n elements xi such that Summation(xi*wn) = 0 Substituting wi value in this equation we get Double Summation((xi*aji)*vj) = 0 It has m equations and n unknowns To solve we need no. of equations >= no. of variables hence n<=m