6 Let (u, v) be the inner product on R² generated by A = - [ -1 and let u = (3, −5), v = (7,4). Find (u, v). (u, v) = 1 -2 ]

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.

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A: We find coordinate of new position

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Q: Find curl (2z i + 3x j + 5y k). curl (2z i + 3x j + 5y k) (i )i + ( i j+ ( i )k

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Q: Show that (x, y) = 5x1y1 – 9x2y2 for vectors x = (x1, x2) and y = (y1, y2) in R2 defines an inner…

A: This question is about application of linear algebra

Q: Show that V spans P² where V = {1 + 2t + 2t², t + t², 1 − t²}

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Q: Find 4rye®y? dA, where R [0, 1] × [0, 2]. R

A: The objective is to find the double integration where  R=[0,1]×[0,2]

Q: Find curl (9z i + 10x j + 5y k). curl (9z i + 10x j + 5y k) = ( i )i + ( i j + ( i

A: Curl

Q: Find curl (7z i + 8xj+2y k). curi (7z i+ &x j+ 2y k) = (1 i+( j +( )k

A:

Q: Prove (z1z2)bar = (z1)bar (z2) bar

A: The objective of this question is to prove that the conjugate of the product of two complex numbers…

Q: a) f(z) = vz+Vz - 1 b) f(z) = Vz2 +9 %3D

A: A branch point of an analytic function is a point in the complex plane whose complex argument can be…

Q: Q/Find the real values of a , b, c that make the convolution equal to zero for the vector function…

A:

Q: Given the function g of the two real variables t and u by g(t,u)=t^2 + tu-u^2+(6+2)u c) Determine…

A: Linearization of a function g(t,u) about (a,b) is  L(t,u)=g(a,b)+(t-a)gt(a,b)+(u-b)gu(a,b)

Q: ) Differentiate: Y(u) = (u-2+u-³)(u³ + 3u?) и и

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Q: ulo,3) = 1+ y 1) u'xg U(x, o) = 1+x 2

A:

Q: Translate Q (0, -8) using (x, y) → (x - 3, y+ 2). Your answer: O Q'(-2, 5) Q' (3, - 10) O Q'(-3, -6)…

A: The transformation is, (x,y) ------> (x-3, y+2) So, (0, -8) ------> (0-3, -8+2)

Q: If X = U+v , y =U-V then Show that + 2 du? = 2) ( %3D nene Than ded uce that wok cu+ v*+ (u+v) g…

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Q: Determine the values of y such that D(9,3,-2), E(3,4,7) and F(21,y,-20) are collinear

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Q: Why do we get cov(y0, y0) instead of cov(yt, yt)

A: Given MA(3) process

Q: 25) Which notation describes the translation of the sailboat B(70, 20) to the lighthouse B'(10, 80)…

A: Given: B70,20, B'10,80 For reaching from point B to point B', we have to use operation x,y⇒x-60,…

Q: show that the function 3x²y-y³ ty is he harmonic and then find it's Harmonic conjugate v (x, y)

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Q: Determine whether the function f(z)=z^2+(bar z) is analytical at z=1+i, where (bar z) denotes the…

A: Analytical functions, also known as holomorphic functions, are complex functions that are…

Q: Find curl (2z i + 3x j+ 2y k). curl (2z i + 3x j+ 2y k) = )i + ( i )j + ( i i )k

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Q: 5 - 25 + Z² = -1 2x + 34 = 2 -y-27 = 0 (Mabrices), find of 2 Rom Rescaling

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Q: Understand Properties of the Cross Product Given u x = (-4,-3, 4), find (u - 5v) × (ū+3v).

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Q: z is a complex variable z=x+iyFind all points of discontinuityf(z)=(3z^2 +4)/(z^4 -16)

A: To locate the points of discontinuity of the given function f(z) of the complex variable z.

Q: If F = ⟨F1, F2, F3⟩ what is div (curl(F))

A: F = ⟨F1, F2, F3⟩

Q: S 22² +2+1 dz, where с Z² +4 b) Compute i) ( = {Z : 121=1} ii) C = {z: 17-i |=2} 17 (iii) C = {z :…

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Q: Lemma*: If z(x, y) = W+H, then xZx + y2y = (xWx+yWy) + (xHx + yHy).

A: Solution:

Q: + xln\ V 1 – x° | dx

A: