Example 1:- if x=u(1-v),y=(uv) then verify that a(u,v) a(x,y)-1 a(x, y) a(u,v)

Q: Calculate û x ô if û = ĵ + 2k and û = -i - ĵ + k. %3D

A: Topic = Vector   if u→ =a1i+a2j+a3k and v→ =b1i+b2j+b3kthenu→×v→=ijka1a2a3b1b2b3

Q: Find u v, uu, |v||2, (u v)v, and u. (3v). . u = 8i + j - 3k, v = i - 4j + 3k (a) u. V (b) u. U (c)…

A: This question is related to vectors, we will solve it using given information.

Q: Find u · v, u· u, ||v||2, (u · v)v, and u · (3v). u = (3, 11), v = (-4, 3) (a) u: V (b) u. u (c)…

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Q: 1 2 0 0 2 0 0 2 0 0 plain why span M2(R) 0 4 3 4

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Q: Construct a Formal Proof of validity: (Ǝx) Ux ⊃ (y)[(Uy v Vy) ⊃ Wy] (Ǝx) Ux • (Ǝx) Wx ∴(Ǝx) (Ux •…

A: Given that (Ǝx) Ux ⊃ (y)[(Uy v Vy) ⊃ Wy] This means there is x which satisfies the conditions. The…

Q: Find u. v, uu, ||u||², (u - v)v, and u . u = , V = (a) (b) u. V u . u (c) || u ||2 (e) (d) (u. v)v…

A: “Since you have posted a question with multiple sub parts, we will provide the solution only to the…

Q: calculate v × w.v = v = (1, 1, 0), w = (0, 1, 1)

A: Given v=<1,1,0> and w=<0,1,1> v×w=i→j→k→110011         =i→(1-0)-j→(1-0)+k→(1-0)…

Q: Transform the equation: 2x2y'' + xy' + 3y = 0 to the form of: a(d2y/dz2) + b(dy/dz) + cy = 0 (a,…

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Q: Find u · v. u - (7, 2) - (-6, 3) V u.v -

A: Since you have asked multiple questions in a single request so we will be answering only first…

Q: Find u · (v x w). (4, 4, 4) (4, 6, 0) w = (0, 0, 9) u = V =

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Q: 5 -2 3 Which of the following could be a value for v? Suppose that - = -20 and that u = a) v = b) v…

A: Given that , u→.v→=-20 and u→=5-23, Now we have to find the value of v→.

Q: xy* Let f (x, y) = if (x, y) # (0,0) and f (0,0) = 0. (a4+6y8)

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Q: Suppose that u × v = ⟨1,0,4⟩. Find (2u−3v) × v.

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Q: Find u · (v x w). u = (4, 0, 0) v = (9, 9, 9) (0, 4, 4) w %3D

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Q: ample3:lf x = u(1 – v) , y = uv , then verify %3D a(u,v), a(x,y) at: a(x.y) a(u,v) =1 H.W

A: It is jacobian problem

Q: Calculate the cross product assuming that u x w = (6, 3, 6) (-u+3w) x w =

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Q: Consider the following. u = (-5, 5, 4) v = (0, 1, 6) Find u x v.

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Q: What is the image of C? C B C' A B' A'

A: Solution is given below:

Q: Using Baye's Theorem, show that if X⊥Y, then I(X;Y|Z)=I(X;Y,Z

A: Using Baye's theorem, show that if X⊥Y, then  IX, Y/Z=IX, Y, Z.

Q: Find u · v, u · u, ||v||². (u - v)v, and u · (3v). u = (3, 12), v = (-2, 3) (a) u. v (b) u.u (c)…

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Q: Find u v. = (9, 2) v 3 (-8, 4) V: U V D

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Q: Suppose ū = (-4, 1) and ū = (0,4). Then: u+0= u - D= 0 - u= 4u= 4u – T0=

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Q: d) If U = X + Y and V = Y – X, find i) The Jacobian value of U and V J(U,V)

A: Solution

Q: Let R (s, t) = G (u (s, t) , v (s,t)) where G, u, and v are differentiable, и (1,2) — 5, из (1, 2) —…

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Q: 5) Find ôw/ôv if w=x² +(y/x), x u-2v+1, and y= 2u +v-2, at the point (u, v) = (0,0)

A: We have to find all partial derivatives first.

Q: translation: 3 units up О гез,0), Л(1, ), К (0, 1) ТО, 3), Т4, 4), К (3. 2) T6, 3), J(-1, 2), K'(0,…

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Q: Let W(s, t) = F(u(s, t), v(s, t)), where F, u, and v are differentiable, and the following applies.…

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Q: vektor u = (1,0,0) and v = (0,12,0) find u x v and ||u x v||

A: vektor u = (1,0,0) and v = (0,12,0) find u x v and ||u x v||

Q: IF x = f(u, v), y =g(u, v) then gu fugv-fugu au 8x

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Domain

In simple mathematics terms, a domain is defined as the space on which all the possible inputs for the function will lie. It can also be expressed as a set of departures for the required function.