a) Define a mapping T:R* → R³ by [2a-b] =b+c T c+d i) Determine whether T'is a linear transformation. ii) Find the image of v 11 iii) Find the preimage of z = 4 -1

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Q: Determine whether the given transformation is linear or not? T(x, X2, X3) = (X1,X2, XzX3)

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Q: In Question, determine whether T is a linear transformation.

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A: We use definition of linear transformation.

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A: T:Rn→Rm: by T(V)=AVGiven A=0-10-1T(V) =AVIf.let V = x1x2 T x1x2=A x1x2=0-10-1 x1x2= -x1-x2…

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Q: Let -9 D 1.7₁ and Y2 -3 -12] and let T: R² R² be a linear transformation that maps ₁ to ₁ and maps 2…

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Q: Let T: M2x2 → P2 is a transformation defined as follows: b 7(₁2)=a+ = a + (b+c) x + (d + C Determine…

A: I have given the answer in the next step. Hope you understand that

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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: Let T :U → V be a linear transformation. Use the rank-nullity theorem to complete the information in…

A: The given table is - We know that dim(U) = dim ℝm×n = m×n For ℝ1×2 dim (U) = 2 Using rank nullity…

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Q: 3) Given the mapping T: R² → R³ defined by T(x1 , X2) = (3x1 – 2.x2, 4.xj + 5x2, x1 –x2) a) Prove…

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Q: Define a mapping T:R³ → Rªby - y (ED). x+y y-z 3z i) Determine whether T' is a linear…

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Q: a) Let T: R4 → R³ be a linear transformation. 2 --0--0-0--0-0 3 -1 -1 Find T 1 3 -2 -3 if T and T 1…

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Q: d) Find the Möbius transformation that maps. ii) i 0, -3 → 6+2i, ∞ → 2i

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Q: Find (a) the image of and (b) the preimage of for the linear transformation. T: R³ → R³, T(v, V2,…

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Q: a b = a² + b² (b) c d

A: (b) Given that, Tabcd=a2+b2 To find whether the given T is linear transformation. (i)…