| № |
Condition |
free/or 0.5$ |
| m97385 | Use membership tables to establish each of the following:
(a)
(b) A ∪ A = A
(c) A ∪ (A ∩ B) = A
(d) |
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| m97399 | Use property (2) of Theorem 2, with D the standard basis of IR", to find the inverse of:
(a)
(b) |
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| m97408 | Use the Cauchy-Schwarz inequality in an inner product space to show that:
(a) If | u || < 1, then (u,v)2 < ||v||2 for all v in V.
(b) (x cosθ + y sinθ) y2 < x2 + y2 for all real x,y, and θ.
(c) ||r1v1 + - + rnvn||2 < [r1 ||+ - + rn|| v||]2 for all vectors v" and all r, > 0 in R. |
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| m97418 | Use the dot product in R" unless otherwise instructed.
In each case, verify that B is an orthogonal basis of V with the given inner product and use the expansion theorem to express v as a linear combination of the basis vectors
(a)
(b)
V = R3, (v, w) = VTAw where A =
(c) v = a + bx + cx2, B = {1, x, 2 - 3x2}, V = P2, (P, q) = P(0)q(0) + p(l)q(l) + p(-1)q( -1)
(d) |
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| m97419 | Use the Euclidean algorithm for polynomials to find the gcd of each pair of polynomials, over the designated field F. Then write the gcd as s(x)f(x) +t(x)g(x) where s(x), t(x) ( F[x].
a) f(x) = x2 + x - 2, g(x) = x5 - x4 + x3 + x2 - x - 1 in Q[v]
b) f(x) = x4 + x3 + l, g(x) = x2 + x + lin Z2[x]
c) f(x) = x4 + 2x2 + 2x + 2, g(x) = 2x3 + 2x2 + x+ 1 in Z3[x] |
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| m97420 | Use the fact that every polynomial equation having real- number coefficients and odd degree has a real root in order to show that the function f: R → R, defined by f{x) = x5 - 2x2 + x, is an onto function. Is f one-to-one? <br> </span> </div> </div> <!-- Google Adword Banner--> <div class="google-adword-banner"> <div class="adword-banner"> <script async src="//pagead2.googlesyndication.com/pagead/js/adsbygoogle.js"></script> <!-- question_page --> <ins class="adsbygoogle" style="display:inline-block;width:730px;height:90px" data-ad-client="ca-pub-4274030376980924" data-ad-slot="7315349492"></ins> <script> (adsbygoogle = window.adsbygoogle || []).push({}); </script> </div> </div> <!-- Relevant Question Section--> <div class="related-question-section"> <span class="related-question-section-heading">Students also viewed these questions</span> <br> <br> <!--Question--> <div class="related-question-statment"> <span class="question-icon-complete-placement"><img src="includes/images/rewamp/question_membership/supported-images/Q_small.png" class="image-text-positioning"></span> <span class="no-padding question-statement-complete-placement"> <span class="related-question-statement-styling"><a href="/for-a-a-b-c-let-f-a-">For A = {a, b, c], let f: A × A be the closed binary operation given in Table 5.6 |
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| m97434 | Use the Gram-Schmidt process to find an orthonormal basis for the subspace of R4 with basis |
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| m97435 | Use the Gram-Schmidt process to find an orthonormal basis for the subspace of R4 with basis.
coefficient matrix is not square or is nonsingular. Determine whether this is the case in your software. If it is, compare your software s output with the solution given in Example 1. |
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| m97436 | Use the Gram-Schmidt process to transform the basis
For the subspace W of Euclidean space R3 into
(a) An orthogonal basis;
(b) An orthonormal basis. |
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| m97437 | Use the ideas developed at the end of the section to confirm the result obtained in (a) Example 13.2; and (b) part (a) of Exercise 2. |
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| m97439 | Use the information in Table 14.11 to compute each of the following in Z30.
(a) (13)(23) + 18
(b) (11)(21) - 20
(c) (13 + 19)(27)
(d) (13)(29) + (24)(8) |
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| m97450 | Use the method of exhaustion to show that every even integer between 30 and 58 (including 30 and 58) can be written as a sum of at most three perfect squares. |
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| m97460 | Use the properties of Section 3.2 to prove that |
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| m97465 | Use the recursive definition given in Example 6.15 to verify that each of the following strings is in the language A of that example.
(a) (())()
(b) (())()()
(c) ()(()()) |
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| m97466 | Use the recursive technique of Example 3.9 to develop a Gray code for the 16 binary strings of length 4. Then list each of the 16 subsets of the ordered set {w, x, y, z] next to its corresponding binary string. <br> </span> </div> </div> <!-- Google Adword Banner--> <div class="google-adword-banner"> <div class="adword-banner"> <script async src="//pagead2.googlesyndication.com/pagead/js/adsbygoogle.js"></script> <!-- question_page --> <ins class="adsbygoogle" style="display:inline-block;width:730px;height:90px" data-ad-client="ca-pub-4274030376980924" data-ad-slot="7315349492"></ins> <script> (adsbygoogle = window.adsbygoogle || []).push({}); </script> </div> </div> <!-- Relevant Question Section--> <div class="related-question-section"> <span class="related-question-section-heading">Students also viewed these questions</span> <br> <br> <!--Question--> <div class="related-question-statment"> <span class="question-icon-complete-placement"><img src="includes/images/rewamp/question_membership/supported-images/Q_small.png" class="image-text-positioning"></span> <span class="no-padding question-statement-complete-placement"> <span class="related-question-statement-styling"><a href="/for-positive-integers-n-r-show-that">For positive integers n, r show that </a></span> </span> </div><div |
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| m97467 | Use the result from Exercise 23 to develop a formula for the average of the entries in an n-vector
In terms of a ratio of dot products. |
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| m97505 | Use Theorem 7.2 to write a computer program (or to develop an algorithm) for the recognition of equivalence relations on a finite set.
Theorem 7.2
Given a set A with |A| = n and a relation R on A, let M denote the relation matrix for R. Then
(a) R is reflexive if and only if In ≤ M.
(b) R is symmetric if and only if M = Mtr.
(c) R is transitive if and only if M ∙ M = M2 ≤ M.
(d) R is antisymmetric if and only if M ⋂ Mtr ≤ In. (The matrix M ⋂ Mtr is formed by operating on corresponding entries in M and Mtr according to the rules 0 ⋂ 0 = 0 ⋂ 1 = 1 ⋂ 0 = 0 and 1 ⋂ 1 = 1 - that is, the usual multiplication for 0 s and /or 1 s.) |
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| m97507 | Use truth tables to verify that each of the following is a logical implication.
(a) [(p → q) ∧ (q → r)] → (p → r)
(b) [(p → q) ∧ ¬ q] → ¬p
(c) [(p ∨ q) ∧ → ¬q] → ¬ q
(d) [(p → r) ∧ (q → r)] → [(p ∨ q) → r] |
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| m97520 | Using a Ferrers graph, show that the number of partitions of an integer n into summands not exceeding m is equal to the number of partitions of n into at most m summands. |
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| m97525 | Using inverters, AND gates, and OR gates, construct gating networks for
(a) f(x, y, z) = x + y + x
(b) g(x, y, z) = (x + z)(y + ) |
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