B =: 0 -4 A = -1 3 1 1 C = -3 & & Find ??? 1- Prove that At + Bt + Ct = (A+ B + C)t %3D 2- Prove that (B * C)t = Ct + Bt 3- A-1 B 4- -3B-1 + Bt

Q: ds if s = Find dt 7t + 3 ds dt II

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Q: Equating the coefficients of corresponding powers of t gives 2/3(13A2 + 2) = 10A2 + 1, (2.200)…

A: 2313A2+2=10A2+1   .....(1)2935A3+10A2=10A3+2A2     ...(2) We need to solve the equations to find the…

Q: (a) Show that xn → x and Yn →y implies Xn + Yn → x + y and also show that an -→ a and Xn → ax. → x…

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Q: В. Let a %3 -в -2 1, Find a value for k so that the dot product of a with = Lk 1 4]is zero.

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Q: Residue of at z = -3 is (z+3)² Select one: a. -2 b. 2 C. 3 d. -1 е.

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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: v.(AX 8) - 8 ·/TXA) – A (vX 8) Prove the earuation.

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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: 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: 3. Prove that {12a + 4b |a, b e Z} = {4c\c € Z}.

A: as per our guidelines we are supposed to answer?️ only one question. Kindly repost other question as…

Q: The set of of solution of x2 - 5x+ 6 0 in Z12 is (a ).{2,3,4} d){2,3,6,11} (b) {2,3} (c) {.2,3,6}

A: Hence option (b) is correct.

Q: Let 1 A = - [3 +1], B =[ _4], 0 = [1] -2 3 (a) Show that AB = CB. (b) Can we cancel B from both…

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Q: verify that (A + B)T = AT + BT

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Q: 23. If u = f(x), then +2x² + 1 k + C for some constant k . x² + 1 Compute kf (1). (a) ¼ (b) – ½ (c)…

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

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Q: /2 5b) What is ll xl)=(2 ²) if x= G,s%2;X3=--) toce where -n/2 2. and Xn = L?

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Q: A national consumers’ association determines that x years after its founding in 1998, it will have…

A: Given: P(x)=2x3-45x2+264x(a) Since between 2000 and 2013 (2≤x≤15)P'(x)=ddx(2x3-45x2+264x)We know…

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: A = -1 3 1 -4 1 C = -3 2 & B = 3. & 6. Find ??? 1- Prove that At + B* + Ct = (A +B + C)* 2- Prove…

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Q: 2 Let A B = -1 |0 and C = 7 Find x, y,z | 2 -3 such that AB =C.

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Q: 5. (a) Find the real constants P, Q, R, for which 3 P Qx + R x2 – x + 1° x3 + 1 x + 1 | Show that V3…

A: 5(a)  3 / (x3+1) = P/(x+1) + (Qx+R)/(x2-x+1) ......(1) Now, 3/ (x+1)(x2-x+1) = P/(x+1) +…

Q: find A1 ∩B1 , GIVEN THAT                                             U= {x ∈ z/ - 7}    A= {x ∈ Z+…

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Q: 1 1 b. From (i) prove that, xb + x ² + 1 + x² + x ² + 1 ² + 1 = 1 xa +x+b+1 c. From (ii) given in…

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Q: 24. Find the first approximate solutions for -2x? + 4x + 2 = 0. 1 - and x = 3- 3 3 x = and x = 3- 3…

A: -2x2+4x +2 = 0Dividing Both the Sides by -2x2-2x-1 = 0Since the coefficient of x2 is 1Move the…

Q: Q3: If you replaced the coefficients of x1, x2, and x3 by 50, 20, 10 What is your final JJI Jguz lio…

A: Here, We have to replace the coefficient of x1, x2, x3 by 50,20,10 Than we have to answer the…

Q: Consider z1 = 1- j2 and z2 = -2 + j3. What is the result of 5z1 + 3z2? %3D -1 -j O 1-j none of the…

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Q: Prove indirectly: "V n E Z, 4 ł (n² – 2)."|

A: Ans:Let us assume that 4/n2-2;∀n∈zthen we have there exist a positive integer k such…

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: 4. Prove that if f(x) = agx" + a,x"-1 +..+ an-1x = 0 has a positive root x = xo, then the equation…

A: Note that f0=0 and that fx0=0. So using mean value theorem there must be some 0&lt;λ&lt;x0:…

Q: 1. Using Gauss-Jacobi, compute a solution to the problem Ax=b where 2-4 7 3 2 49 -2 A = 8 7 b= 16 23

A: Given : A =2-4783249-2      b=71623                  AX= b To find : The solution of problem by…

Q: In what case of k such that there is only one solution? 2x + ky = 10 kx + 2y = -10

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Q: 21. Find af and of if f(x,4)= 3x" +2xy+ Sy , x= 4v? + Bn", and u 2v-w? Vour %3D 4= 2v-w? Vour av…

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Q: 3 1 -1 2 -4 -3 1 C = 2 A = & & 5 6. Find ??? 1- Prove that At + Bt + Ct = (A + B + C)t %3D 2- Prove…

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Q: T: M22 ---&gt;M22 defined by T(A) = AB,

A: Given, a matrix B, and defined a map T(A) = AB, where T: M2×2  ---&gt; M2×2. We have to find the…

Q: f(2) = x-4I satisfies the hypothesis of Rolle's Theorem on 0, 8. [0, 8]. Select one: a. True b.…

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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: 2 In x 1 e* 2 1 In 2x -1

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Q: (*") = (") + G) + 5. Prove + 2n2. %3D

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Q: 10- The general solution for the PDE (2D, +3D, -6)(D, – 3D,=0 is u(x, y) = e"ExG,(3x-2y)+G,(-2x-y),…

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Q: & B= Q1-Let A = 2 4 Verify that (AB)" = B" A"

A: As per our guideline we are supposed to do 1 question at a time. Please post other questions next…

Q: a- If A = -1 %3D 2 and B = -41 prove that (A + B)T = AT + B". 12 [1/2 - If A-1 =1/2 -1/2) and |A| =…

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Q: JJ. JUA X ABD) 224 ABE) 16 36. g(x)=2x -3x² +5x+3 ACD) 1 АCE) 2 37. h(x)=x -4x³ +3x² +8 ADE) -3 BCD)…

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Q: 2) x+y+kz= 2 3x+4y+2z=k 2x+3y-z =1 a) for have only one solution ks b) for be unsolvable k? c)…

A: Step:-1 Given system of equation is x + y + k z =23 x + 4 y + 2 z =k2 x +3 y -z =1 11k34223-1 xyz =…

Q: 4. Show that: do Tb/(a? – b²) - a+bcos0 а b2 Where a>b>0 such that * -1+ 1. < 1 - a²

A: To Show: ∫0πdθa+bcosθ=πba2-b2 Concept: i. 1+tan2x=sec2xii. cos x=1-tan2x21+tan2x2iii.…

Q: Show ther' 3 2

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