Let u = (1, 2, 3), v = (4, 4, –2), and w = (6, 5, -5). Find z, where 2u + v - w + 3z = 0.

Q: Find a and b such that v = au + bw, where u = (1, 2) and w = (1, -1). v= (6, 9) a = b =

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Q: Express ∂w/∂r and ∂w/∂s in terms of r and s if w = x2 + y2, x = r - s, y = r + s.

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Q: Let q (y, z) = (2y + 13) * (29 − z). Calculate ∂q/∂y and ∂q/∂z

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

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Q: Find (a) u × v, (b) v × u, and (c) v × v.…

A: Given : u =0,2,1v = 1,-3,4(a) u x v = ijk0211-34u x v =i 21-34    -j0114  +k021-3          = i(8+3)…

Q: Given F(r, s, t) = r(3s4 – 6t°), compute: Frst

A: This is a partial differential problem

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

A: Given: Two vectors are . In part (a) Find the vector product of two vector u and v. therefore the…

Q: Express the following as a linear combination of u = (2, 1, 3), v = (1, -1, 4) and w = (3, 2, 6).…

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Q: Let f(r, y) = (3 – y)". Then %3D drdy drðydr

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Q: Express the following as a linear combination of u = (6, 1, 7), v = (1, -1, 4) and w = (1, 8, 7).…

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Q: Given that v = and w =. Find

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Q: calculate r'(t) and T(t), and evaluate T(1). r(t) =〈3 + 4t, 3 − 5t, 9t 〉

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Q: Find (a) u + v, (b) 2v, (c) u − v, and (d) 3u − 2v. u = (1, −2, −3), v = (3, 1, 0)

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Q: Let F(x,y,z) = 3x²y + 6y³ – 5xz². Find VF ,V²F¸ K×VF, and V×VF.

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Q: Express the following as a linear combination of u= (3, 1, 7), v = (1, -1, 7) and w = (6, 3, 6).…

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Q: Let u = (1, 2, 3), v = (2, 2, −1), and w = (4, 0, −4).Find z, where 3u − 4z = w.

A: u = (1, 2, 3)3u = (3×1, 3×2 , 3×3)3u = (3, 6, 9)v = (2, 2, -1)w = (4,0,-4)

Q: Find (∂z)/(∂s) and (∂z)/(∂t), given: (c) z = x2 + 2y2 ; x = es - et, y = es + et

A: Formula to find the partial derivatives helps to find the partial derivatives of the function with…

Q: 4. If possible, express t as a linear combination of u, v, and w. t = (2, 13, 5), = (1,2, 1), v = (-…

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Q: Let u = (1, 2, 3), v = (4, 4, -2), and w = (6, -1, -2). Find z, where 2u + v – w + 3z = 0. z =

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Q: Find a and b such that v = au + bw, where u = v = (7,2) a = b || || = (1, 2) and w = (1, -1).

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Q: Let u = (1, 2, 3), v = (2, 2, -1), and w = (4, 3, -4). Find z, where 2u + v - w + 3z = 0. z =

A: Given :u=(1,2,3)v=(2,2,-1)w=(4,3,-4)

Q: b) If x = u(1 + v) and y = v(1+u), find vx, Ux and a(u,v) a(x.y)

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Q: Find r' (2), where r(t) = u(t) × v(t), with u(2) = (1, ,2, – 1), u' (2) = (3, ,0, 4) , and v(t) =…

A: Solution :-

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

A: Let's consider w = (a, b, c, d) So w + u = (a, b, c, d) + (1, -1, 0, 1) = (a + 1, b - 1, c, d + 1)

Q: Determine if b is a linear combination of ā1, ãz and dz. 6 = 2 3 16

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Q: Be z = (x-y)/(x+y), where x = (u/v), y = (v2/u), calculate ∂z/∂u and ∂z/∂v

A: The given equation is z=x-yx+y where, x=uv, y=v2u. Find the value of ∂z∂u and ∂z∂v. Here we use the…

Q: Find a and b such that v au + bw, where where u (1, 2) and w - v- (0, 6)

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

A: Given , u=1,-1,0,1v=0,2,3,-1and 3 w=u-2v

Q: Given: z = = x* + zy°, * = ww* + w, y = u +ve" a z Find when u = - 3, v = 2, w =

A: Given: z=x4+xy3x=uv4+w4y=u+vew The objective is to find ∂z∂u, when u=-3, v=2, w=0

Q: Suppose u=, v x +y and w w(u,v): a) Express W, and W, in terms of W. W. X and y b) Calculate XW,…

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

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Q: Find 2 (v x u), given u x v = (-, 5, 8). %3D

A: u×v=-83, 5, 8

Q: Find a and b such that v = au + bw, where u = (1, 2) and w = (1, -1). v= (4, 5) a = 3 b = 1

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Q: Express the following as a linear combination of u = (4, 1, 6), v = (1, -1, 5) and w = (4, 3, 8).…

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Q: (b) Let h(x, y, z) = x?y+ yz?, where a = u + v, y = u – v and z = -u. Calculate and ди dv

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Q: Find a and b such that v = au + bw, where where u = (1, 2) and w = (1, -1). v = (0, 24) V = a = b =

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Q: Express the following as a linear combination of u = (3, 1, 6), v = (1, -1, 8) and w = (5, 5, 7).…

A: Let's find.

Q: Find (a) u + v, (b) 2v, (c) u − v, and (d) 3u − 2v. u = (−1, 2, 1), v = (0, 1, 1)

A: Given  u = (-1,2,1) , v = (0,1,1)Find   (a) u+v      (b) 2v      (c) u-v      (d) 3u-2v

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

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Q: Given, o (x, y, z) = 3x²z – z²y³+ 4y°x² – 2y + 4z – 1, find V²¢. O 6z + 6y3 – 6z²y+ 24x²y 6x 12z +…

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Q: a(x, y) r = u? -v,y =ue". Compute ô(v,u)

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Q: Express the following as a linear combination of u = (6, 1, 7), v = (1, -1, 4) and w = (2, 6, 4).…

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Q: find ƒx , ƒy , and ƒz . ƒ(x, y, z) = xy + yz + xz

A: Given: fx,y,z=xy+yz+xz

Q: Let V = {A, B, C} and T= {0, 1}. Find a) VXT b) T²,T³3,T4

A: Given V = {A,B,C} and T = {0,1} we have to find a) V × T b) T2 , T3, T4

Q: Let u = (1, 2, 3), v = (2, 2, –1), and w = (4, 3, -4). Find z, where 2u + v – w + 3z = 0. Z =

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Q: If f(z) = z² - (z)² + zz, calculate the following: a) u(x, y) and v (x, y) b) u(-10,-5) and…

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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…