Compute Div(F) and Curl(F): F--(4y-1) i+yj+(-3y) k

Q: 3. a) Describe the transformations on y = 3* to sketch y=-2(3)+1

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Q: Show that the into R² defined by T₁ = ( 9₁ ₂1₂) — 172,9₁) and T2: (F₁, F₂) → (Y¶₁₂ Y {₂) : are…

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Q: Let R = {(x,y): |x| + |y| ≤ 2}. Use the transformation x=u+v, y=u-v to evaluate ∫∫ ((x^2)*(e^y))dA

A: Consider the given: R=x,y:x+y≤2x=u+vy=u−vA=111−1=−1−1=−2=2

Q: Decomposition fields are algebraic extensions.

A: Definitions:Decomposition fields(splitting field) :  A splitting field of a polynomial p(X) over a…

Q: SLo(xy) dA where R is bounded by 9x2 + 4y² = 36 %3D Use the transformation: x = 2u and y = 3v

A: The given region R is: 9x2+4y2=36...(1) To use the transformation: x=2u,y=3v So, equation (1)…

Q: For 3 and 4given the translation rule: T(x,y) (x+2,y-3)

A: Find the image of (5,-1) and preimage of (-6,7)

Q: Find an LU decomposition of 7-779 A= -1 -1 11 7 1-3 -1 21 -1 17 15

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Q: assume thatf (2, 3) = 8, fx (2, 3) = 5, fy (2, 3) = 7 Which of (a)–(b) is the linearization of f at…

A: Consider the given: f2,3=8fx2,3=5,fy2,3=7,

Q: Yi 6x1 -1x2 Y2 —17х1 +3x2 I|||

A: Given linear transformation T is  y1=6x1-1x2y2=-17x1+3x2 Its inverses is the function T-1 from y to…

Q: Find the Jacobian of following functions f(x,y,z) = 3xy – yz + 2y³z² – 5xyz³ g(x,y, z) = xyz – x³yz…

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Q: Determine the kernel and the range of the linear operator on L(x) = (x1 + x3, X2, 0)

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Q: nd S √(² (2x + 5y)dA where R is the parallelogram with vertices (0,0), (-2,-4), (3,-5), and (1,-9).…

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Q: Explain how to compute the Jacobian of the transformationT: x = g(u, v), y = h(u, v).

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Q: |-2+1 () 7:2 だ,て メ-ドコ X, +1メ」 メレ-3x, transformation is gi ven t of trensformation; 4) Show that it…

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Q: Complete the description of the transformation rule: (x, y) → ( x + 7, y - 15) Translate and

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Q: 1 Under the transformation w=-, find the image of y – x + 1 = 0

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Q: Calculate 121x dxdy where R is the parallelogram with vertices (0,0), (6,2), (7,6) R 1 -(v — Зи), у…

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Q: under the linear transformation T: R² → R² consisting of a reflection in the y-axis followed by a…

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Q: Let be the map sending each complex number 三→ Ly that f (2,2,) = f (2,)f(2) Show

A: The detailed solution is as follows below :

Q: Determinar si los ángulos son coterminal 70, 430

A: In trigonometry, two angles in standard position are said to be coterminal if they share the same…

Q: y)(Ty → Wy) - Hv)) → Ia

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Q: Each of J, K, L, M and N is a linear transformation from R? to R². These functions are given as…

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Q: 3. Each of J, K, L, M and N is a linear transformation from R2 to R. These functions are given as…

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Q: Let →a=⟨7,−5⟩ and b→=⟨1,3⟩. Compute the dot product. →a X →b=

A: Given a→ = 7,-5 and b→ = 1, 3. We have to compute the dot product a→·b→.

Q: Which of the following transformations are linear? А. Т В. Т 8 x + 2 С. Т y, D. T z. 7y Е. Т -4z -9x…

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Q: 6. (10) Is the transformation defined by T(x1, x2) = (2x1, 3x1 – 5x2, -x2 + 1) linear? Explain.

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Q: Let T be a triangle with vertices (1,-2), (3,0), (-3,2), and f(x,y)=x^2(y-x+3) (a) Find the linear…

A: It is given that T is a triangle with vertices 1,-2, 3,0 and -3,2 and the function fx,y=x2y-x+3. (a)…

Q: use the given rule to transform the figure and identify the type of transformation given by each rul

A: The given figure is