Find (a) the image of v and (b) the preimage of w for the linear transformation.T: R2→R3, T(v1, v2) = (v1 + v2, v1 − v2, 2v1 + 3v2), v = (2, −3), w = (1, −3, 4)

Q: 5. T: P3R, T (a₁ + a₁x + a₂x² + a3x³) = a₁ + a₂ Answer

A: Kernel is the elements of P3 whose image under transformation T is zero in R.

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A: Given that   and

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Q: Find the kernel of the linear transformation.T: P3→P2, T(a0 + a1x + a2x2 + a3x3) = a1 + 2a2x + 3a3x2

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Q: Find the inverse of the linear transformation X1 = x2 = x3 = Y1+ Y₁+ Y1+ Y1 Y2 Y3 = = = 4x1 5x1 X1…

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Q: Does this equation define a linear transformation from R3 to R2?

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Q: Find the Jacobian of the transformation = 2u+7v, y u² - 5v. =

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Q: Find the Jacobian of the transformation x - 3u + 7v, y = u² – - v.

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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: A ||

A: T:P2→P2 defined by  Tft=f9t+6

Q: Find the Jacobian of the transformation a = u² + 5v², y = 7uv

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Q: If v = (v1, v2) and T(v)=v except T(0, v2) = (0, 0) then T(v + u) = T(v) + T(u) showing that the…

A: Linear with respect to addition is given. We have to prove for scalar multiplication.

Q: Find (3x + 2y)dA where R is the parallelogram with vertices (0,0), (4,5), (-3,1), and (1,6). Use the…

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

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Q: Find the matrix of a linear transformation that would take the line 2x -5y = 0 to 7x -3y = 0

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