1) Suppose T is a linear transformation of TH=2-3x + x² and T[3] =1-x² T[2¹] and T Determine. R² to 8₂ so that

Q: 2a + 56+ c -a – 36 – 2c) 3a + 7b +c -4a – 96 - c, 2. T(а + bx + сх*).

A: The solution is given by using rank nullity theorem and null space as follows :

Q: IfT: R³ R³ is a linear transformation such that --- then T 5 → 0-80-80-4 T

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Q: The image of the transformation T(x) = Ax defined by 12 A 4= [(2₂4] is the line in R² of all scalar…

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Q: 4. Let T: R" → Rm be a linear transformation and suppose T(u) = v. Show that T(-u) = -v.

A: Since T is a linear transformation, for any scalar number c, we must have,        T(cu) = cT(u)

Q: (C)- [-5x1 + 9x2] 4x1 – 7x2 T:R² → R² is a linear transformation, such that T Show that T is…

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Q: - Evaluate f√x+y (y-x)² dxdy using the transformation x+y=ky D.

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Q: Let T be a linear transformation from M2,2 into M2,2 such that ([D-[-] ([:D)-[; ²] ([: :)) - [1 ²];…

A: Given :T1000=1-102T0100=0211T0010=1201T0001=3-110

Q: 3. Consider the linear transformations T : R² → R² and S: R? → R² defined by 7 (E)-E :(E)-L] [2x2 X2…

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Q: .Define f: R- R by f(x) = rx + d, where r and d are real constants. Show that for f to be linear, it…

A: Given:

Q: 17. Let T R2 R2 be a linear transformation that maps : u= [5] in •[3]. 2 3 T is linear to find the…

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Q: Define the linear transformation T by T(x) = Ax. Find ker(7), nullity(7), range(7), and rank(7). 3 3…

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Q: 21. Let T R² T(x1, x₂) T(x) = R2 be a linear transformation such that (x₁ + x2, 4x₁ + 5x2). Find x…

A: Please check the answer in the next step. This is very straight forward.

Q: Which of the following transformations are linear? Y1 = -10x1 OA. Y2 = 6x1 Y3 = 3x1 OB. ( OC. Y2 Y3…

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Q: Show that T: R² → R4 is a linear transformation, where T is given by 2x2 3x1 4x2 T ((:))-[***] = X2…

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Q: ppose that T : R² → R² is a linear transformation and that 7([일) -B] T and ar (H) nd T

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Q: Let T: R² → P₂ be a linear transformation for which [1]-1-]-*+ = 1 - 3x and T = x + 3x². -3 a Find…

A: Given that         T : R2 --> P2 be a linear transformation for which T(1,1) = 1-3x and T(2,-1) =…

Q: Draw a transformation diagram for v = (3/5)c, with the numbers 1, 2, and 3 (in meters) on the…

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Q: 3. Explain why whenever A is Ax = 0 always has linear transformation, solution

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Q: [1 The columns of 3 = 0 O Suppose that T is a linear transformation from R³ into R² such that T(e₁)…

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Q: Suppose y = f (x) is transformed to the function y = 2f [- 1/3 (x + 2) ] - 4. Write this as a…

A: Given query is to write the mapping of the transformation of f(x)