Suppose T: R+→P3 is a linear transformation. Let u, v, and w be the vectors given below, and suppose that T(u) and T(v) are as given. Find T(w). Use the 'A' character to indicate an exponent, e.g. 5x^2-2x+1. -5 -5 V = -5 W = -7 T(u) = -9x3+14x²-5x-12 T(v) = 25x3 –36x²-9x+4 u = %3D LO N

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.

Q: (ED) F 3x1 + x2 - 6x3 -x₁ + x₂ +13x3

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Q: a) T: M, → R, where M, is the vector space of n by n matrices over a field, and T (A) = det(A).

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Q: Determine whether the function L: P2 → P2 defined by L(a0 +a1x+a2x2) = a1 +2a2x is a linear…

A: The given function is: L:P2→P2  such that:La0+a1x+a2x2=a1+2a2x

Q: Determine whether the following transformation from R3 to R² is linear.

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Q: Find the inverse of the linear transformation Y1 Y2 Y3 = = = 2x₁ 2x₁ x1 +4x₂9x3 +3x₂ -7x3 +2x₂ - 4x3

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Q: Write v as a linear combination of u1, U2, and u3, if possible. (If not possible, enter IMPOSSIBLE.)…

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Q: Let L be the line in R3 that consists of all scalar multiples of the vector 1 Find the reflection of…

A: As per our guideline we are supposed to answer only one asked question.kindly repost other question.…

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Q: Example : Define a linear transformation T:R² → R² by T(2) = [: [ X1 - 2 | 1 X2 X1 Find the images…

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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 d (3x + 5y)dA where R is the parallelogram with vertices (0,0), (5,3), (4,-2), and (9,1). R Use…

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Q: Select one or more: O a. The function R → R’ which maps a number x to the vector ū = (x, 2x, x²) O…

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Q: A ||

A: T:P2→P2 defined by  Tft=f9t+6

Q: Find the transpose of the matrix.

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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: 3. Let B = Consider T : R2,2 → R²,² defined by T(A) = AB – BA. Let [o o] Bị and B2 :

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Q: Determine whether 2 4 are linearly independent.

A: The vectors are independent if a120+b11-1+c142=000 which implies a=0,b=0,c=0…

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

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