Compute u x v. (a) u = 2i + 3j+ 4k, v = -i+ 3j – k (b) u =i+ k, v = 2i + 3j – k (c) u =i-j+ 2k, v = 3i – 4j +k 27 (d) u v = -2u 1 ||

Q: Calculate F. dĩ, where C is the square of (1,1, 1), (–1, 1, 1), (–1, –1,1) and (1, –1,1), with…

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Q: Calculate F . dr, where C is the square of (1,1, 1), (–1,1, 1), (-1,–1,1) and (1,–1,1), with…

A: Let F→x,y,z=zex-yezi→+2cosy-xezj→+ex-xyezk→ and C is the square with vertices…

Q: 4. For the linear canonical system x' = Jx, x € R², determine the nature of the origin as a fixed…

A: Given canonical system x'= Jx  Case-1:-  det >0 if both Eigen value positive:- The product of the…

Q: In Exercises 47-50, verify that Wy %3D Wex- 47. w In (2x + 3y) 48. w = e + x In y + y Inx

A: NOTE-  As per our guidelines we have to solve only first question. Given data- w = ln ( 2x + 3y ).…

Q: Q1. Use Cramer's rule to solve for y without solving for the un- knowns x, z, and w. 4x + y+ z+ w= 6…

A: use cramer's rule to solve for y withoutsolving for the unknowns x,z and…

Q: Use the method of separation of variables to solve: (ôu ôu - = 0 in (0,1) × (0,+∞), (2) u(0,t) =…

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Q: Use Cramer's rule to solve for y without solving for the un- knowns x, z, and w. 4x + y+ z + w= 6 .…

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Q: Use the chain rule to evaluate fu and f, at (u,v)=(2,-2) where f(x,y,z)=y³+xz² and x=x(u,v)=u+v²,…

A: Concept: The chain rule for the function f (x,y,z) is  dfdu=∂f∂x∂x∂u+∂f∂y∂y∂u+∂f∂z∂z∂u…

Q: Find the Wronskian of a given set {yı, y2} of solutions of 7. (1 x2)y"-2xy' (a 1)y0, _

A: Consider the given equation.

Q: Use the method of separation of variables to solve - V²u = 0 in (0,1)² ×(0,+∞), - |u(x,0,t) =u(x,1,…

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Q: 2x+ 3y-z =1 4x + y-3z = 11 3x-2y +5z = 21 | %3D

A: Solution:

Q: Two functions u and r of x and y are said to satisfy the Cauchy- Riemann equations if u, = v, and -…

A: Given that the functions u and v are said to satisfy Cauchy Riemann equations if ux=vy   and uy=-vx…

Q: Use h=1 to approximate U(1) and U>(1) for the system %3D Uj = -2u2, Ui (0) = 1, u2(0) =1 using the…

A: Please check step 2 for the solution.!

Q: If z = f (u) + g(v), where u = = and v = x ·y. Prove that Q1: x· Zx – y· Zy = y² · Zyy – x² · Zxx…

A: We have z=fu+gv, and u=xy  and v=x.y We need to use the chain rule and prove x.zx-y.zy=y2.zyy-x2.zxx…

Q: Compute (S ,g) where f(t)=1– 3r² , g(1)=t-ť'onV = C[0,1]. %3D

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Q: 2. Solve V'u = 0 for r<1, 0<z< T, u(r, 0, 0) = 0, a7(r, 0, 7) = 0, - u(1, 0, z) = z cos³ 0.

A: It is given that

Q: (b) Find the Wronskian W[y1,Y2](t) of y1 and y2-

A: W[y1,y2]= -t2et

Q: If z = f(u) + g(u), where u = = and v = x · y. Prove that x · Zx – y · Zy = y² ·Zyy – x².Zxx using…

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Q: 2x+ 3y-z =1 4x + y-3z = 11 3x- 2y +5z =21

A:

Q: Use the Chain Rule to find az/əs and ôz/Ət. z = tan(u/v), u = 8s + 3t, V = 3s – 8t

A: z=tanuv,   u=8s+3t,   v=3s−8tFormula→∂z∂t=∂z∂u⋅∂u∂t+∂z∂v⋅∂v∂t

Q: 3. Verify that the vector X is a solution of the given linear system. dx = -x – 2y dt cos 4t – sin…

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Q: find the linearization at x = a. y = (1 + x)^−1/2, a = 0

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Q: (ii) Verify Cauchy-Goursat theorem for f(z) = 5 sin 2z if C is the square with vertices at 1土も-1土。

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Q: Verify, if u = x + y+ z, v = x° + y° + z³ – 3ryz, w = x²+y² + z? – xy – yz – za are functionally…

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Q: Find the linearization L(x,y,z) of the f(x,y,z) = 6sqrtx^3+y^3+z^3 at the point (1,2,3).

A: The linearization of a function f(x,y,z) at a point (a,b,c) is given by the expression;…

Q: The linear operator T: R2 --> R2  defined by T (x; y) = (4x + 5y; 2x + y) is it diagonalizable?

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Q: Minimize c = s + t + u subject to 3s + 2t + u ≥ 48 2s + t + 3u ≥ 48 s + 3t + 2u ≥ 48 s ≥ 0, t ≥ 0, u…

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Q: Use Cramer's rule to solve for y without solving for x, z, and w. 5 x + y + z + W = -7 5x + 3y - z +…

A: Here we have to use cramer rule for solving the system of linear equations

Q: 9. Solve u +u =0 for 0≤x≤1, 0≤ y ≤1, given u(x,0)=0, u, (x,1)=0, u(0, y) = 0, XX yy u(1, y) = 1.

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Q: find the linearization at x = a. y = (1 + x2)^−1/2, a = 0

A: We find the derivative of the given function using power rule and chain rule

Q: s the linear operator T : R3 --> R3 defined by T (x, y, z) = (2x - 3y + 7z, 5y + z, -z)…

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Q: Find (x ,y, z) by using Jacobi or Gauss of Gauss Jordan method 5z — Зу + х%3 -1 2y – z = 2 z - 4x =…

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Q: Compute the weak solution to the problem (a(x)u')' – u = x _for x € (0, 1), u(0) = u(1) = 0 , 1 with…

A: For the solution follow the next steps.

Q: 5. Compute the solution to the original system of equations by transforming y into x, i.e., compute…

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Q: Let T(z) = -6z* +z² –1 and U(x) = 2z – 4x + 3. Find T(z) +U(z) %3D OA. -6z4 + 2z3 +z² - 4z + 2 OB.…

A: Let Tx=-6x4+x2-1  and Ux =2x3-4x+3

Q: If z = f(u) + g), where u = = and v = x· y. Prove that y x: Zx - y Zy = y? Zyy – x2 - Zxx using the…

A: We have to prove this

Q: 2- Find x, y, z, u, t, v such that 2 3 8. 3 5 +2 9 8 14 a) X =-6, y = -1,Z = -1, u = 1,t=2,v= 2 %3D…

A: xyzutv+2123456=8359814   To find : the value of x, y, z, u, t

Q: solve for w where u = (0,-1,1,1) and v = (3,0,-1,2) 5w = u-3v w=

A: Given that, u = (0,-1,1,1) and v = (3,0,-1,2) 5w = u-3v

Q: Solve for r and y the following system of simultaneous equations 2 In(z) = In(y) + In(16) %3D e e =…

A: Solution: As per given data e have two simple equation, 2ln(x)=ln(y)+ln(16) exey=e4 where,'x' and…

Q: Q1. Use Cramer's rule to solve for y without solving for the un- knowns x, z, and w. 4x + y+ z+ w= 6…

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Q: Compute the x's for the system *) = kx k3(x3 – X2) = k2(x2 - X) | k4(x4 - x3) = k3(x3 - x2) %3D F =…

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Q: Let u=2i+3j-2k and v=-1i-4j +k Find u . v, ||u|| and u . v

A: Given that u and v vector and we find its dot product (u.v) and mode of u(||u||). Here i attached…

Q: Consider the linear DE system æ' = Aæ with -14 -90 and A = 2 14 If the initial conditions are given…

A: To find the solution for the below linear differential equation system. x'=−14−90214x,  x0=02

Q: Minimize c = s + t + 2u subject to s + 4t + 2u ≥ 95 4s + t + 3u ≥ 95 s ≥ 0, t ≥ 0, u ≥ 0. c= (s, t,…

A: the given simplex problem is as follows  Minimize c=s+t+2u subject to…

Q: 19: Find two linear operator T, and T,on V(R) such that T,T, = 0 but T,7, - 0.

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Q: on vectors for t2 0.

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Q: Solve for z using cramer's rule.  2x-y-z=4 4x+y+z=2 3y+z=2

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Q: Find the null space associated with the equations: 2x+z+w = 0 7x-6y–z–w-v = 0 -5x+4y+w = 0

A: