Let u = (1, 2, 3), v = (2, 2, −1), and w = (4, 0, −4).Find 5u − 3v − 1/2 w.

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Q: O Find the linearization Lcx) for fex) 3x -8x+7 when a=

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A: The given differential equation is dydt-ay=0 , a∈R.we will slove this by the method of  separartion…

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Q: Let v = 2i - 5j and w = -4i + 3j. Find v . w

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A: Let's find.

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A: A vector F→ is said to be irrational if and only if cure F→ =0 i.e∆ x F→ = 0Given F→ = (axy+bz3) i^…

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A: This is a problem of complex analysis.

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Q: Solve for x, where u = (1, −1, 2), v = (0, 2, 3), and w = (0, 1, 1). 2x − u + 3v + w = 0

A: Given u = (1, −1, 2), v = (0, 2, 3), and w = (0, 1, 1). And 2x-u+3v+w=0 Plugging the values,…

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Q: ... Solve for w where u = (-1, 1, 1, 0) and v (-1, 2, 3, 0). 3w = u- 4v W 3=

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Q: If A = x° yz? î – 3x² z³ j + yz? k , then a² A at the point (1,0, 1) will be дхду 3 î -3) -3 î

A: The vector A is A=x3yz2i-3x2z3j+yz2k find ∂A∂y=x3z2i+z2k ∂2A∂x∂y=3x2z3i the point 1,0,1…

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A: Let,

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

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Q: Express w as a linear combination of u and v. 1 - 5 u = V: w = - 9 w = u+

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Q: Solve for w, where u = (1, −1, 0, 1) and v = (0, 2, 3, −1). 1/2w = 2u + 3v

A:

Q: To find ∫x3(x4−15)7dx∫x3(x4−15)7dx, you would need to use u-substitution. What u could be used to…

A: ∫x3(x4-15)7dx

Q: Q4\ If A(x,y, z) = 3x²i + 3zj – 3xk find the Div (Grad A). %3D |

A: Explanation of the answer is as follows

Q: Solve for w where u = = (0, 1, 1, –1) and v = (0, -1, 2, 3). %3D 5w = u - 4v W =

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Q: If u = ex+₂y+azz, Show that d² u əx² + where a₁, a2, as are constants and a² + a² + a² = 1. J² u 8²…

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Q: Find dw/dr and dw/dΘ for w=2z/y-3x if x=3Θ+2r, y=3r^2 + Θ, and z =4r-Θ, where Θ = 2 and r = 5.

A: w=2zy-3xx=3θ+2r,y=3r2+θ, z =4r-θTo find ∂w∂r and ∂w∂θ for θ=2 and r=5

Q: If z = x + y, x = 2t, y = 3t, then %3D %3D 1 5 II

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Q: 2. v(t) = c1cos(wt) + c2si=

A: Differential eq:1.x(t)=t2+ctx'(t)=2t+cx''(t)=2This is the required differential equation.

Q: Solve for x, where u = (1, −1, 2), v = (0, 2, 3), and w = (0, 1, 1). 3x + 2u − v + 2w = 0

A: The given vectors are Let the vector x be

Q: Let u = 2i−j+3k, v = 3i+j−k, and w = 3i+j+2k. Verify Equation (3).

A: Given- u=2i-j+3k,v=3i+j-k and w=3i+j+2k To verify- The equation u×v·w=u·v×w

Q: wx + yz = bc, for z II

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Q: Find the solution of BVP 2. Uxy = 4xy+ex ; uy (0,y) = y, u(x,0) = 2

A: uxy=4xy+ex uy0 ,y =y u(x,0) = 2 To find solution of given differential equation

Q: Find (a) u × v, (b) v × u, and (c) v × v. u = 2i + k, v = i + 3k

A: Given that, the two vectors u = 2i + k, v = i + 3k To find the following (a) u × v, (b) v × u, and…