1. (a) Use definition of linear transformation to determine whether the transformation T: R - R defined as follows is linear. -y a+ 2y 2r – 4y

Q: 3. Let T: R² R2 be a linear transformation such that T H]-[ = -5x1 + 9x2 4x17x2 Find T-¹.

A: T:ℝ2→ℝ2 is a linear transformation  Tx1x2=-5x1+9x24x1-7x2

Q: Find the standard matrix for the linear transformation T: R² 3 and then reflects about the line y…

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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:R" R" be a linear transformation, and let {V1, V2, V3} be a linearly dependent set in R".…

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Q: If T : R3 → R3 is a function which has the property T(ax + by) = aT(x) + bT(y) for all a, b ∈ R and…

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Q: Define the linear transformation T by T(x) = Ax. Find ker(7), nullity(7), 2 2 A-1-2 2] -2 2 (a)…

A: A=22-22 we have to find Ker(T), Nullity(T), Range(T) and Rank(T)

Q: Prove or disprove whether the transformations T defined below are linear. (i) T(x1, X2, X3) %3 (хз —…

A: Answer

Q: Suppose T is a linear transformation, with T(7) = = Find the following: T( – û) = T(4u - 7v) = [³].…

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Q: 2. Let L2 : R3 → R² be defined as L2(x) = L2 (x1, 2, X3) = (x1 + 0.3x2, x3 +2). Is L2 a linear…

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Q: Let f be the linear transformation represented by the matrix 2 -2 A = (2) 3 -2 Find the point (x, y)…

A: Given, A=2-23-2 Need to find the point x,y such that fx,y=-4,-1.

Q: Let T: R² →R² be a linear transformation that maps u = 3 5 2 -1 into and maps v = into - [ ] [ ³ ] […

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Q: Determine whether or not the following linear transformation is invertible, and justify your answer

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