The linear Diophantine equation 11x + ny = 44 is solvable if, and only if, gcd(11,44)|n n = gcd(11,44) n|44 nE Z

Q: Use Gauss-Jordan Reduction to find the value of the unknowns in the given set of equations. -7 1 3 +…

A: We can solve this using gauss Jordan reduction method

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Q: 1) Prove that there are no positive integer solutions to the equation x2-y?=1

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Q: 1. Show that for all z1, Z2 E C, Then we have: |Z1 + Z2| < |Z1| + |Z2|

A: Using complex properties.

Q: Find the two smallest positive solutions of 5sin(5x)=3

A: 5sin(5x)=3 sin(5x)=.6 sin(5x)=sin36.87°

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Q: Also, from Theorem 4.9', we have k2k-1 k2k [(E – 2)(E – 1)(E +2)]¬!2* (4.239a) (1 · 4)(1!)…

A: The one is red is [(E-2)(E-1)(E+2)]-12k=k2k-1(1*4)(1!)=k2k8        (1)y(P)k=-79k-k26+k2k8…

Q: 1. If x=27-3k and y = i +5j -4k, express each of the following in terms of i, j, k b) 2(3x+y)-3(4y…

A: Given x→=2i→-3k→ &amp; y→=i→+5j→-4k→To write expression in terms of i→,j→,k→:

Q: 2. Solve the following Cauchy problem: Uu = Uzz -0 0, u(x,0) = x – a², u(x,0) = 4x, -00 <x < 0. %3D

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Q: 1. Find the general solutions of 2z = 3 c. In+2 + In+1 – 2z, = (-2)*+1, a. In+2 + In+1 b. In+2 +…

A: solving difference equation, xn+2+xn+1-2xn=3 by changing auxiliary equation we get, E2+E-2=0 By…

Q: The set of solutions to z =-V2 - V26 is

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Q: The solution of e² = - 11 has the form x + ily + 2nn) where n is an integer. What is the value of x?…

A: The given equation is                                                ez=-11

Q: 10- Solve the problem: Utt-4uxx = xt, 00 u(x,0) = x, 4(x,0) = 0, u(0, t) = 0, Ux(1,t) = 1+t, t20 %3D

A: Given, utt-4uxx=xt;   0&lt;x&lt;1, t&gt;0 ⋯⋯⋯⋯1ux,0=x,   utx,0=0,   0≤x≤1,⋯⋯2u0,t=0,   ux1,t=1+t,…

Q: How many integer solutions are there to the equation x1+x2+x3+ x4 25 subject to x; > i? Let y. X,-\,…

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Q: 26 If A = then det(A) is Zero %3D %3D -5 4 Choose Zero Nonzero Thus, A 1 and det(A 1) =

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Q: Compute Re if z₁ = 5√√2 + 2√3i, and z2 = 3√√√2-5√3i 2

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Q: Show that \{e ^ (- x), x * e ^ (- x)\} is a fundamental set of solutions of y^ prime prime +2y^…

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Q: Solve The following Syslem equations of liner 1t 44. 21 = 8 - 3n 12y - 62 = 6 Sn+74-52= 6 Solve by…

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Q: Prove or give an counterexample to the statement that for any neZ+ and aeZn, the equation +n X = a…

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Q: 8 (2-15)*- 3-V5 (a) Express in the form p + q5, where p and q are integers. (b) Given that = ab°,…

A: To solve the given problem we use the following result (a - b)2 = a2 + 2ab + b2 , (a+b)(a-b) = a2 -…

Q: 8. Work out a Gaussian quadrature formula of the form Ans. A; = 1, x; = Aif(x1) + Arf (x2). f(x) dr

A: The given problem is to prove the following integral, the proof is to show the 2 point gaussian…

Q: Show that for all z1, Z2 E C, Then we have: |Iz1| – |z2|| < |z1 +z2l

A: 2) The inequality can be proved as follows:

Q: 3. Find the constants bo, co, a1, b1, C₁ so that So(x)=1+ box + cox² + x³, S(x) = { S₁(x) = a₁ - 2x…

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Q: Theorem 9 Let {um}=-5 be a solution to Eq. (18) and suppose that u-s = a, u-4 = b, u_3 = c, u_2 = d,…

A: We are asked to show the following equation, u8n-3=c2ne2n∏i=12nic+a∏i=12n-1ie+c Using the identity,…

Q: 1. Show that for all z1, Z2 E C, Then we have: |Z1+ Z2| < ]Z1] + |z2|

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Q: 3.41 Show that the Neumann problem in x'+ y? < 1 au = 2 an on r'+ y = 1 does not have a solution.

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Q: Prove that if b+ 6 < 0, then x + bx + 5= 0 has at least one real solution.

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Q: Solve the followig 13. BauSsian or Eduss Jordan Using E lemination. 5x, +6x=7X 3D0 3. ース×,+ 3X7…

A: Answer

Q: The least positive solution modulo 330 for the system х3D 1(тod 5) х%3D 2(тоd 6) x = 3(mod 11) is x…

A: Chinese Remainder Theorem: If m1, m2, .., mk are pairwise relatively prime positive integers and if…

Q: Use Gauss-Jordan Reduction to find the value of the unknowns in the given set of equations. 2 1 3 9…

A: As per the question we are given a system of nonlinear equations in variables x, y, z, w And we have…

Q: (2) Determine k such kx? – 4x +÷= 0 that has real and different solutions. 2

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Q: 1: Find Z by convolution theorem. (z- 2)

A: convolution theorem

Q: and such that the sum of their squares is as small as possible. Give the sum of the squares.

A: Given problem:- 2. Using Lagrange multipliers, find three positive numbers whose sum is 18 and such…

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Q: Show that 1 is the only solution of x25 - 1 = 0 in Z37.

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Q: Show that the equation In(x + 1) = In(x²) has at least two real solutions.

A: we need to show that ln(x+1)=ln(x2) has at least  two real solutions.

Q: 4. Use Cramer's rulc to solve the lincar systemn. r+ 3y 2 5.r +7y 3

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Q: (a) Show that any finite linear combination of the solution of following n th -order difference…

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Q: 1. Lat A - [; : - and B = 2 2 1 3 4 (a) Compute AB. (b) Compute BA.

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Q: The linear Diophantine equation 11x + ny = 44 is solvable if, and only if,

A: We are given the linear Diophantine equation 11x+ny=44. For it to be solvable we must have gcd(11,…

Q: 4. what is the cofactor of the following. a. C34 bC12 c. C32 d. C21 1 2 0 3 0 1 8 5 5 4 -2 3 -3 1…

A: As per guidelines we can solve only three subparts at a time so if you need more answers kindly…

Q: If t,= 4n+1, find t,, t,, t3, and t Express t n+1, in its simplest form. n+1 In-1

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Q: 10. Find all solutions of the system of congruencies x = 2 mod 3 x = 4 mod 5 х З тod 7

A: Use Chinese remainder theorem Answer and explanation is given below

Q: Therefore n-1 ( fsi+4P + föi+3h foi+3P + fei+2h ) (foi-19+ fei-2k , feiq + fei-1k Tên-3 = k| i=0…

A: Given : In Theorem 4,                 fmm=-1∞=1, 0, 1, 1, 2, 3, 5, 8, ......... We need to explain…

Q: 2. Solve the following Cauchy problem: u, + 2ru, - u=a+3ye" with u= 2r - 1 on y=-

A: We have to solve the given Cauchy problem.

Q: 4. Find the dual of the following LP: max z = - 4x1 - X2 4x + 3x2 6 X1 + 2x2 s 3 3x1 + x2 = 3 s.t.…

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Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.