I da By making the linear transformation 21 = y₁ ay2, 22 = 2y1 + y2 S[y1, y2] = = dx [y² + 2y2 + (2y1 + y2)²].

Q: Compute foxy dx + (x³/2+y³/2) dy where C is the square with vertices (0,0), (0,1), (1,1) and (1,0)…

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Q: 3 х. 0 -2 T(x) %D Find the matrix M of the inverse linear transformation, T-1. M =

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Q: Use the transformation u = x - 2z, v = 3y, and w = z to evaluate 7 9 2z+3 ICE 2z Submit an exact…

A: Introduction: The process of determining the area of the region under the curve is known as…

Q: D7 + D® – 2D$ – 2D4 – 7D³ – 7D² – 4D – 4) y = 0 - - - -

A: follow next step

Q: Determine the intersection of 3x – 4y – 5z = 0 with [x, y, z] = [3, 1, 1] + t [2, -1, 2].

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Q: Т: M22 —} R where (1: а — За — 46 +с — dis a d. T C linear transformation.

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Q: Q3: Evaluate z+ 2ydA where R is the triangle with vertices (0,3), (4, 1) and (2, 6) 1 1 using the…

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Q: Find the Jacobian of the transformation. x = 8e³+, y = 6e³-t a(x, y) à(s, t) =

A: To find the Jacobian of the following transformation. x=8es+t, y=6es-t

Q: TR2 → R2 as, T x, y = (1, y) ;is it a linear transformation?

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Q: Consider the linear transformation: D: P, (R) P(R) given by D(p(z))=P(z)j. Equivalently, D(p(x)) =…

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Q: Evaluate ff(6x - 3y)dA region bounded by the parallelogram with vertices (2, 0), (5, 3), (6, 7) and…

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Q: T(x, y, z) = (x + y, z-1)

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Q: Which of the following transformations are linear? DA. T(A) = A + Is from R³x3 to R³×3 OB. T(A)=9A…

A: Given :  A.TA=A+I3B. TA=9AC. T(A)=A2 To Check : Given transformation is linear Note : As per policy…

Q: Show that T(x, y) = (x - y, y (x - 1)) is not a linear transformation from R² to R².

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Q: Show that the transformation T3(x, y) = (x + y, -x + y) is the inverse of T₁. T₁(x, y) = (x - 2y, x…

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Q: Find the Jacobian of the transformation x = 5u - 5v, y = u² – 2v —

A: Jacobian of transformation for two variable ∂x,y∂u,v=∂x∂udxdv∂y∂u∂y∂v ............(1)

Q: Evaluate I= √ (sinx+2y) dx + (6x+y)dy for the non closed path ABCD in the figure.

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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: For a linear transformation w= (atib)z, the point A= (1+j) in the z-plane was transformed to A' =…

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Q: Find the rank and nullity of the T(ƒ(t)) = t(ƒ'(t)) from P₂ to P₂ transformation T.

A: Given the transformation  T  from  P2 to P2 i.e.   T : P2 → P2 given by ,            T(f(t)) =…

Q: Given the following linear transformation T: R³ R³, T(x, y, z)=(x-2y, 0, 2x - 4y). Find the core and…

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Q: CD has coordinates C(-8,-2) and D(-4,-12). determine the coordiantes of C'D' if (x,y) -> (1/2x,1/2y)…

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

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Q: Calculate the nullity n(T) for the linear transformation T defined by T(r, y, z) = (r+ 2y + 2, -r+…

A: Given : a linear transformation T defined by  Tx, y, z=x+2y+z, -x+3y+z   To find : nullity nT

Q: linear transformation A maps P(1,0) to P’(-2,-4) and Q(0,1) to Q’(4,1). Find (i) The matrix A (ii)…

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Q: If L: R² R³ be defined by L(x, y) = (x, y, 1), show that it is a linear transformation.

A: Introduction: A linear transformation is a function from one vector space to another that respects…

Q: Find Joy²dx + (xy-x²) dy along C: y = 7x from (0,0) to (1, 7).

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Q: Q8) Find the Linearization f(x.y.z) = x² + xy + yz +? at (1,1,2)

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Q: 2 [1]},e2 = [1 ], v₁ = [3], and y₁ = [¯-1]," e₂ 5 6 R² be a linear transformation that maps e₁ into…

A: We are given that           T(1, 0) = (2, 5) and T(0, 1) = (-1, 6)  Now,          (5, -3) = 5(1, 0)…