Find all mER such that for the solutions it is 12+1

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

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

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

Q: If TeZx Such that x is a momber of 27+5x-3=03 and S={x Such that x i. member of 2i+71+233/3 that T…

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Q: Let A = LU, where L is lower triangular with 1’son the diagonal and U is upper triangular. How many…

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Q: For which values of a and m does ax = 1 have a solution in Zm?

A: Claim:

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

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Q: For all n ≥ 1, let an = (a) Find a1, a2, A3, A4. (b) Computea. i=1 (c) Computea. i=1 (n + 1)² n!…

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Q: B = and C: .Prove that A = B² =C? = 1. 3. Given A = %3D

A: Given: A=0110, B=0-ii0, C=100-1 We know that for a 2×2 matrixP=abcd, P2 is given by…

Q: Given that (z-N(z-n=6z-221, where z=x+yi and z is the conjugate of z. Solve for x and y 28 and y=3…

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Q: Prove that if gcd(a,b)=1 then gcd(a+b,ab)=1.

A: Given, gcda,b=1 Let, d=gcda+b,ab This implies, da+b and dab This gives, dba+b⇒dab+b2Since,…

Q: Suppose x,y,z are mutually coprime positive integers that solve x2+y2=z2. a) Show why exactly one…

A: Basic properties of modular arithmetic and gcd will be used in solving this problem. The detailed…

Q: Find all the numbers z such that e^2iz= 5i.

A: We are given : e2iz=5i Now Using  Euler's equation: ( eix=cos x+i sinx) ⇒e2iz=cos (2z) +i sin(2z)…

Q: Show that the solution (if exists) is unique:

A: Given, u =6x + 4y +2 on {x² + 4y² <1} u(x, y) = x+2y+y²-4xy²-8y³ on {²+4y²=1} Using maximum…

Q: Use the substitution method to show that the solution of T(n) = 2T(n/3) + n2is O(n2)

A: Given that T(n)=2Tn3+n2 To show that it is O(n2).

Q: the associateu mCs are paamei. 6. Find the DE of y = ax2 + bx + c by eliminating the arbitrary…

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Q: (2) Find all the numbers z such that elz = 10i.

A: Consider the given. eiz=10i

Q: Find the length of Kl. K %3 %3D

A: Given,

Q: solve each non linear Sys tem of eauati ons analyticaly for all real Solutlons. x2 ス+ tyd =4

A: We need to solve x2+y2=4, and 5x2+5y2=28. For x2+y2=4: We know that x−a2+y−b2=r2  is the circle…

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. Classify the following PDE, reduce it to the canonical form and then find its solution: 1 Uzz -…

A: Hyperbolic pde

Q: Solve the Fol| owing linear ryctems completely and nece ssary solutions. Computations. show all 3x 2…

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Q: Prove the part of the theorem which lets w be any solution of Ax = b, and defines V = w- p. Show…

A: Let W and p be the soln of Ax =  b i.e, Aw = b,  Ap= b so, w=p+Vn ⇒ Vn = W-p Now,  AVn =…

Q: Find ATA and AA". 2 0 1 %3D -1 4 2 (a) ATA 1 1 (b) AAT 21 Which of the products are symmetric?…

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Q: Find the value(s) of k such that A is singular.

A: A matrix is singular if its determinant value is zero. So we find the determinant value of the given…

Q: nd all values of z for which zª + 2 – i2/3 = 0 and represent them geometrically. |

A: To solve the given equation by using D'Moivre theorem we find the point. The 4 value of z satisfy…

Q: Find the wronkian of 64 w(t)= W Cyi s Yo)

A: Given: 64y''-36y=0

Q: the integret fector of the bifferentiel e qration →き x28x he is 2. O Not found

A: Consider the given differential equation xdy-ydx=x2y3dx and rewrite it again by doing…

Q: Suppose x-j, for j-0, 1, 2, 3 and it is known that Find Po123(1.5). P₁1(x)=x+1, P₁2(x)=3x-1, and…

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Q: Consider the following IVP: x" - 4x' + 4x = 4e2t; x(0) = -1, x'(0) = -4 %3D %3D

A: We have to solve the given differential equation,(IVP).

Q: Find A'A and AA". -1 1 4 A = 2 0 2 (a) ATA (Б) ААТ Which of the products are symmetric? (Select all…

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

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Q: Find the least value of “n" so that , k=n 1 199 Sn 2k-1 k=1 200

A: Given:          Sn=∑k=1n12k−1&gt;199200

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…

Q: Use the branch and bound method to solve the following IP: max z = x₁ + 2x₂ s.t. x₁ + x₂ = 10 2x₁ +…

A: use the branch and bound method to solve the following IP max z=x1+2x2s.tx1+x2≤102x1+5x2≤30x1 ,…

Q: Which of the following is a fundamental set of solution of y" – 2y' + 5y = 0.

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Q: Find the solution of the following IVP using the characteristic method : u + uu= y у , и(1,у) %3D Зу

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Q: of a 4x7 natrix is H19. The dinansun of the nul at least: space A) 3 B)4c)5 D) 6 E) 7

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Q: ALMN has vertices L(-2, 2). M(2, 3) and N(2, 0) L.

A: Coordinates of L = (-2,4) Coordinates of M = (6,-2) In right angle triangle circumcentre is the mid…

Q: #1 and #2, write a 2-column proof. Given: 5(2x - 8) = 30; Prove: x = 7 %3D 5C2x-8)3D30 Gioen

A: topic:-simplification

Q: 4 and for n > 3, an 2an-1 + an-2 + 5n, express an in terms of n %3D 2. Let, a1 = 3, a2

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Q: 1. For positive integers i, j,n such that i+ j = n (a) show that corresponding multinomial…

A: sol(a) we know that multinomial co-efficient is definedby ni,j=n!i!,j!  —(1) where i+j=nnow…

Q: -:find sup (A) and inf (A) when A= (y = 2x + 1, x € N, -10 < x < 10}

A:

Q: If the statement is true, prove. If the statement is false, disprove. 1 + 2" > 3n for all n E Z

A: False.  take n =2

Q: If z=2e(i pi/20), use De Moivre's theorem to compute z5

A: Use demoivre theorem

Q: Find all m, n E N such that: n! + 2n + 49 = m²

A: This problem can be solved by graphical approach. Use a graphing utility to plot the graph of…

Q: Find the value(s) of k such that A is singular.

A: to find the value of k