From determinant to tensor - download pdf or read online

By W. F. Sheppard

ISBN-10: 1177681315

ISBN-13: 9781177681315

Writer: Oxford Clarendon Press book date: 1923 matters: Determinants Vector research Notes: this can be an OCR reprint. there's typos or lacking textual content. There are not any illustrations or indexes. in case you purchase the overall Books variation of this publication you get loose trial entry to the place you could choose between greater than 1000000 books at no cost. you may also preview the e-book there.

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A. 3x ϩ x Ϫ 1 ෇ 0 B. 8 ෇ x 2 C. 6x ϩ 2 ෇ 9 D. 1 1 xϪ ෇0 2 x 2. Which of the equations in Exercise 1 are nonlinear equations in x? Explain why. 3. Decide whether 6 is a solution of 3͑x ϩ 4͒ ෇ 5x by substituting 6 for x. If it is not a solution, explain why. 4. Use substitution to decide whether Ϫ2 is a solution of 5͑x ϩ 4͒ Ϫ 3͑x ϩ 6͒ ෇ 9͑x ϩ 1͒. If it is not a solution, explain why. 5. The equation 4͓x ϩ ͑2 Ϫ 3x͔͒ ෇ 2͑4 Ϫ 4x͒ is an identity. Let x represent the number of letters in your last name.

The subtraction in the numerator must be done before the division. P Ϫ 2L PϪL 2 EXAMPLE 2 Solving a Formula with Parentheses The formula for the perimeter of a rectangle is sometimes written in the equivalent form P ෇ 2͑L ϩ W͒. Solve this form for W. *Using the distributive property to write ab ϩ ac as a͑b ϩ c͒ is called factoring. See Chapter 6. An Addison-Wesley product. Copyright © 2004 Pearson Education, Inc. 2 Formulas 59 One way to begin is to use the distributive property on the right side of the equation to get P ෇ 2L ϩ 2W, which we would then solve as in Example 1.

The solution set, ͕Ϫ3͖, has only one element, so 5x Ϫ 9 ෇ 4͑x Ϫ 3͒ is a conditional equation. (b) 5x Ϫ 15 ෇ 5͑x Ϫ 3͒ Use the distributive property to clear parentheses on the right side. 5x Ϫ 15 ෇ 5x Ϫ 15 0෇0 Subtract 5x and add 15. The final line, 0 ෇ 0, indicates that the solution set is {all real numbers}, and the equation 5x Ϫ 15 ෇ 5͑x Ϫ 3͒ is an identity. (Note: The first step yielded 5x Ϫ 15 ෇ 5x Ϫ 15, which is true for all values of x. ) (c) 5x Ϫ 15 ෇ 5͑x Ϫ 4͒ 5x Ϫ 15 ෇ 5x Ϫ 20 Distributive property 5x Ϫ 15 Ϫ 5x ෇ 5x Ϫ 20 Ϫ 5x Subtract 5x.

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From determinant to tensor by W. F. Sheppard

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