2. Give a combinatorial proof of the following identity n 7n6n6i-17n-i = i=1 Hint: Consider strings of length n from the set {0, 1, 2, 3, 4, 5, 6}.

Q: The inverse of matrix A = [100 -98; 98 98] is A^-1 = [-98 99; 99 -100]. Indicate what is the…

A: The condition number of a matrix is = norm of A * norm of inverse of A

Q: The basis for the eigenspace corresponding to one of the eigenvalues of matrix  is ...

A: Given problem: The basis for the Eigen-space corresponding to one of the Eigen-values of matrix  is…

Q: Indicate which of the following statements is true a) The Cholesky factorization of a matrix A…

A: Option (a) The Cholesky factorization of a matrix A exists if and only if A dominant is diagonal; We…

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A:

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A: Here we have to find no of ways a brand of pen can be selected.

Q: Please show your complete solution and write readable thanks. A gardener makes a triangular planting…

A:

Q: Find an equation of the tangent plane to the parametric surface R(u, v) = 〈(u — sin u) cos v, (1 −…

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Q: 1.) xyax ^)/√²-1²) dx + (x² - 2xy) dy = 0

A: Given : x2-y2dx+x2-2xydy=0 To Check : Differential equation is exact or not

Q: Construct a trace table to trace the action of the Euclidean Algorithm for the imput variabless 1570…

A: To Construct: A Trace table for the action of Euclidean algorithm for inputs a=1570, b=488.

Q: Please see image

A: In this question, we have to find an example of a linear operator T such that T is not nilpotent but…

Q: Suppose demand is given by p = 1600 − x. Find the maximum revenue.

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Q: 7. y arccos(cosh(10x))

A:

Q: Prove the following statements. These exercises are cumulative, covering all techniques addressed in…

A: Note: since you posted multiple questions. As per our guidelines we can solve only one problem at a…

Q: 1. Water is poured into a cylindrical tank, and then a spout at the base of the tank is opened so…

A: Given: Water is poured into cylindrical tank . Volume is given by f(t) m3 where t is measured time…

Q: 14. Let (S, d) be a metric space, ACS, and c E S. Prove that c is a cluster point of A if and only…

A:

Q: Identify the surface whose equation in rectangular coordinates is given by x² + y²-2²-4x-6y+12=0.…

A: Given x2+y2-z2-4x-6y+12=0 ∴x2+y2-z2-4x-6y+12=0⇒x2-4x+4+y2-6y+9-z2=1⇒x-22+y-32-z2=1 The equation of…

Q: y³y' + x³ = 0 .3

A: As per our guideline, we are supposed to solve only first question. Kindly repost other question as…

Q: Let S be the set of all symmetric 2 × 2 matriceswith real entries.(a) Show that S is a subspace of…

A: Symmetric matrix: A=AT  Basis is a non-empty set spans the space and linearly independent.

Q: 14. Determine whether f: ZxZ → Z is onto if a) f(m, n) = 2m - n. b) f(m, n) = m² = n². c) f(m, n) =…

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Q: 5. Find the critical values of the function l( : ) = II k=1 constants. ххке xk! Here =…

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Q: Use the improved Euler's method to obtain a four-decimal approximation of the indicated value. First…

A: For h= 0.1 Given y′=2x-4y+2,y(1)=6,h=0.1,y(1.5)=?Here,…

Q: Name: 1. Show the following propositions using a direct proof. (a) Proposition. If a is an odd…

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Q: nstruct the interpolation polynomial ng Lagrange method given the distinc nts for x and f(x). = 1,…

A: Lagranges interpolating polynomial

Q: 2. If a 1 and an+1 for each n> 1. Use the mathematical induction to show the sequence (an) is…

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Q: Use Euler diagrams to determine whether the following argument is valid or invalid. All snakes have…

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Q: Kindly explain what "!" Means. also, provide steps of the equations

A: Factorial of a non-negative integer is the multiplication of all positive integers smaller than or…

Q: 12. Use only the e-6 definition of limit to show that lim (2x²-x) = 6.

A: The given limit is limx→22x2-x=6 We have to prove this limit using ε-δ definition.

Q: Show that for primitive statements p, q, pvq [(p^¬q) v (p^q)] →→(p→q).

A:

Q: Which of the following are solutions to the ODE Show your work Ou(t)= e2t 2u" (t)- 10u' (t) + 12u(t)…

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Q: Show that the group Z13 is cyclic and give all of its generators. List all the distinct subgroups of…

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Q: Let the vector field (x,y)→f(x,y) be Lipschitz in space, let h=0.1, and consider the Euler map g(x,…

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Q: 1. Determine whether or not the following relations are functions. If the given relation is a…

A: we solve these  problems by the help of graphs.

Q: Prove the following for Integers x and y, (17 | 10x + 8y) = (17 | 3x + 16y)

A: 17 | 10x + 8y where x and y are integers => 10x + 8y = 17m for some integer m

Q: Given the function: f(x) = -18x³ + 45, find the equation of the tangent line, or linear…

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Q: The function f(x,y) = 6xy has an absolute maximum value and absolute minimum value subject to the…

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Q: The indicated function y(x) is a solution of the given differential equation. Use reduction of order…

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Q: find the family of parabolas with axis parallel to x-axis

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Q: -(x-11)²+5 if x > 10 3x-15 f(x) = -²² - 6x-6 -3 -x-2 3x + 12 -(x + 5)²-1 -(x + 10)²+5 x + 15 if 8 <…

A: fx=-x-112+5ifx&gt;1032if8&lt;x&lt;103x-152-3if3&lt;x&lt;8-x36x-6-16if0&lt;x&lt;3-x-23x+12if-4&lt;x&l…

Q: 4. Let A € Rnxn, u, v € Rn. Compute the inverse of A = 1 + uv¹. Hint: try a matrix I-auvT with a R…

A: To Find: Inverse of A=I+uvT and constraint on u and v.

Q: Congruence. 1.Find the remainder when 3¹² is divided by 11 2.Find the remainder when 4¹⁰ is divided…

A:

Q: -5/4 -TT -3/4 -TT/2 -TT/4 -7- -6 TT/4 TT/2 c. Give the midline (vertical shift) of the function.…

A: As per the policy of bartleby the provisions is to solve only three sub parts of questions now I am…

Q: 6. Show that the following system cannot be solved with the help of LU-decomposition method. 3x,…

A: The given linear system is ,                 3x1-3x2+x3 =   4-2x1+2x2+x3 =-1    x1+x2+2x3   =    3…

Q: Let v₁ = (1,-1) and v₂=(1,1). Let V=span (v₁v₂). Do v₁ and v form an orthogonal basis for V? 1 2 1…

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Q: Consider f: (0, 2)→ R defined by f(x)=x". Assume that f has a limit at 0 and find that limit. (Hint:…

A: In order to answer this question you need to know the following notions given below

Q: If f(x) = (x5+1)(x4- x) and g(x) = (x3-1)2 then g is O(f) but f is not O(g). Group of answer…

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Q: Prove that the equation ax + b = c has a unique solution where a, b, c constants and a≠0.

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Q: each vertex of gra 7. Prove that the order of any subgroup of a finite group divides the order of…

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Q: Show that the system: - 4x - 2y - y = cost, 2x + x + y = 5 sin 3t, is equivalent to the following…

A: The system is given by:   x¨- 4x- 2y˙-y=cost 2x˙+ x + y¨ = 5sin3t Or the above system can be written…

Q: Given the data points 0 0.25 0.50 0.75 1.0 1.25 1.5 0 -1.2233 -2.2685 -2.8420 -2.2130 2.5478 55.507…

A: As per the question we are given the following ndata table : x 0 0.25 0.50 0.75 1.0 1.25 1.5 y…

Q: Show that (up to isomorphism) A5 is the only simple group of order60.

A: Given : G=60 To Prove : G≃A5