Let w = x dz ^ dx + (y³ + æ³ ) dx A dy be a two-form on R³. Determine the one-form *d(tw), where * is the Hodge star operator in R³. *d(xw) dx + dy+ dz

Q: Let 3 = (X'X)-¹X'Y as shown in class. Let y = w'ß, where w is a column vector. Show that Var(y) =…

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Q: nd the transformation on R' (R3) that reflects at xy-plane, then rota round the z-axis by 90 degrees…

A: Follow the steps below.

Q: Determine the singular points of (x² – 9)?y" + (x + 3)y' + 2y = 0 and classify each singular point…

A: Use the definition

Q: (a) Suppose that k is an odd integer and w is a k-form. Show that w^w = 0. (b) Note: This question…

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Q: Find the two roots of (j)'/2 in rectangular. a) 0.770 + j0.770, –0.770 – j0.770 c) 0.707 + j0.707, –…

A: c

Q: Let F = cos(4t) i + 3tj+ 4t°k and G = t cos(4t) i + t j+4e#k Find the cross product F x G =

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Q: Example// Find the centroid enclosed function Y=6x-x². y = x

A: Extremely sorry for the graphing mistake.

Q: Let f(z, y) — (-(г + ))5. Then | 20(-(x+y))^3 dzðy dzðydz dz²dy

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Q: Compute the inner product = f(x)g(x)dx where f(x) = sin(x) and g(x) = sin(2x)

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Q: Enter a rule for a transformation that maps ASTU to AS 'T'U'. S (4, 3) T (4,-3) → T' U (-4,-3)→U'…

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Q: (a) S,(Iz – il2 – z) dz along the semicircle y = 1+ et“, 0 < t < n; -

A: ∫γz-i2-zdz=∫0π1+eit-i2-1-eitieitdt=∫0π1+cost2+sint-12-1-eitieitdt=∫0π1+cos2t+2cost+sin2t+1-2sint-1-e…

Q: 3 Compute the primitive of w= (z³ - x² z)dx ^dy - x²dx ^ dz + (3y² z - 3xz²)dy ^ dz

A: The primitive of a differential form is also known as its antiderivative. In this case, we want to…

Q: classify > 0²2 8x² +4 dez 2 дуг By usin this rule B²-4AC = 0

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Q: Determine whether the following are linear transformations or not. Justify. (1) L(x) = x + 2 where L…

A: The given maps are,(1)  where (2) where The objective is to determine whether the map is a linear…

Q: fCx)=(1+x)* at X=0 is LUX)=1+ KX + "७) %3

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Q: le can define an operator * : 2'(R?) n'(R?) by defining *dx = dy and *dy = -dx, and extending…

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Q: (2) Sketch the direction field associated to the system I'=x²-y-3, y = y + x² - 5. Include the…

A: sketch the direction field associated to the system    x' = x 2 - y - 3 y' = y + x 2 - 5   include…

Q: find the orthogonal trjectories of x=c^y^2

A: We need to find orthogonal trajectories.

Q: Which of the following are true for A = {(1, 1), (1, 2), (1, 3), (1, 4), (2, 1), (2, 4), (3, 2),…

A: The given set .The given statement .The objective is to determine whether the statement is true or…

Q: 4. Classify and reduce the following equations to a canonical form: (a) yu -x*u, = 0, x>0, y>0. (b)…

A: To classify and reduced in canonical form of the given equation is..

Q: ) 3(x+ y) dx + x(x*+ zy + uy) dy - o t.

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

Q: Let a be a real number and f(x, y) = 5ax?y+ 5xy³. Let v = 3i – j and let Vf(x, y) denote the…

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Q: 1) [sex² 4x² - x² dx 2 dx 2 ਤੇ 3) sex² (4x+²) dx 2) 4) S X dx √4-9x² using Integration by…

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Q: the functional F[y] = [[(y^)² - y² + 4ye™ ]dx such that y(0) = y(7/2) = 0. Calculate the minimal…

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Q: Map the image of Ay=x^(1/2) on the w- plane of transformation w=B *Z^2 Assume all missing or error…

A: Given: Now the given are, On the w-plane of the transformation w=B *Z2, map the image of…

Q: Which of the following mappings does not define a linear transformation A: R^3 -> R^2?

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Q: Use implicit differentiation to find dy/dx. 18) y cos = 4x + 4y - y sin A)- cos B) sin 4y 4y2 D)-…

A: 18.we have y cos(1y) =4x+4y⇒dydx(cos(1y) )+ysin(1y)×1y2dydx…

Q: 11. Evaluate * d²y dy - 2 + 5y = –17sin2x dx2 dx y = (C,e* + 68 |cos2x +(Cze* + 17 sin2x 15 y =…

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Q: 7. The function (x, y)= (2x* + y* )exp + xy' is homogenous in x and y of degree

A: .Given,f(x,y) = (2x4+y4) ey2x +x y3Put y= xSo we get,f(x,x)= (2x4+x4) ex2x +x x3 f(x,x)= (3x4) e0.5…

Q: (ii) e*u + e'u„ = u XX yy

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