Let f : R → R* be defined by f(x) = (x, -8x2, 6x). Is f a linear transformation? a. f(x + y) f(x) + f(y) = Does f(x + y) = f(x) + f(y) for all æ, y E R? choose b. f(cæ) = c(f(x)) = Does f(cx) = c(f(x)) for all c, x E R? choose c. Is f a linear transformation? choose

Q: What is the rank of linear transformation T from R3 to R3 defined by T(x,y,z)=(y,0,z

A: Given: T:ℝ3→ℝ3 is a linear transformation defined by  Tx,y,z=y,0,z Standard basis of ℝ3 is…

Q: One of the following is not a linear transformation (a) T : R² → R³ defined by T(x, y) = (x, xy, x)…

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Q: Let ƒ : R → R be defined by f(x) = 1 – 5x. Is f a linear transformation? a. f(x + y) = f(x) + f(y) +…

A: Substitute x+y for x in the equation fx=1-5x and simplify to calculate the value of fx+y.…

Q: Find the kernel of the linear transformation.T: R3→R3, T(x, y, z) = (−z, −y, −x)

A: Here the given linear transformation Use the definition kernel of the linear transformation

Q: Let f: RR be defined by f(x) = -8x?. Is f a linear transformation? a. f(x +y) =|-8x2-8y2-16xy f(x) +…

A: Thanks for the question :)And your upvote will be really appreciable ;)

Q: Let (x, y, z) E R³ and the transformation T: R³ → R² be given by T(x, y, z) = (2x + 4y, x + 3y + z).

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Q: Let f : R → R be defined by f(x) = 9x. Is f a linear transformation? a. f(x + y) = f(x) + f(y) =…

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Q: Let f : R → R³ be defined by f(x) = (x, –8x², –9x). Is f a linear transformation? a. f(x + y) = f(x)…

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Q: Let f:R2→R be defined by f(⟨x,y⟩)=2y−2x. Is f a linear transformation?

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Q: T is a linear transformation from R² into R². Show that T is invertible and find a formula for

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Q: Let f : R? → R be defined by f({x, y)) = 3x – 3y. Is f a linear transformation? a. f((x1,Y1) + (x2,…

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Q: If T(u + v) = T(u) +T(v), then T is a linear transformation.

A:

Q: Let f : R → R³ be defined by f(x) = (-9x, –2x, –5x). Is ƒ a linear transformation? a. f(x + y) =…

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Q: 5. Prove that the transformation T: R²R defined by T(x, y) = 5y-k is linear only if k = 0.

A: The given transformation is T:R2→R defined by Tx,y=5y-k

Q: Let f : R → R* be defined by f(x) = (–9x, –9x, –6x – 4). Is f a linear transformation? a. f(x+ y) =…

A: Here given that f:ℝ→ℝ3 is defined by f(x)=-9x, -9x, -6x-4 We have to determined f is linear…

Q: 4. Let T:R R be defined by T(z, y, 2) = (4r - 3y+ 4z, z+2y - 2, 5x -y+3z) Show that T is a linear…

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: Let f : R → R° be defined by f(x) = (x, -3x?, 5x). Is fa linear transformation? a. f(x + y) = f(x)+…

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Q: give a counterexample to show that the given transformation is not a linear transformation.

A: Given,   A linear transformation,

Q: Consider the linear transformation T : R2[x] → R2[x] given by T(a + bx + cx2 ) = (a − b − 2c) + (b +…

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Q: Let f : R → R³ be defined by f(x) = (5x, –5x, 5x). Is ƒ a linear transformation? a. f(x + y) f(x) +…

A: A) f(x+y) = < 5(x+y), -5(x+y) , 5(x+y)>  And than  f(x)+f(y) = <5x,-5x,5x> +…

Q: Let f : R → Rbe defined by f(x) = 2x. Is f a linear transformation? a. f(x + y) = f(x) + f(y) = Does…

A: Given that f:R-->R be defined by f(x) =2x .

Q: Find the kernel of the linear transformation.T: R3→R3, T(x, y, z) = (x, 0, z)

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Q: Let (x, y, z) E R and the transformation T: R³ → R² be given by T(x, y, 2) = (2.x + 4y, x + 3y + 2).

A: Transformation is invertible if and only if transformation is square.

Q: Determine whether the linear transformation T: R3 R3 defined by T(x1, x2, x3) = (x1 + x2, x2 + x3,…

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Q: Let F: R3 → R4 be a linear transformation.   f (x, y, z) = (x, x + 3y, x, x + z) Is f bijective?

A: A function f is said to be bijective if and only if it is both injective(one to one) and surjective…

Q: Let T : R" → R" be a linear transformation. T is said to be precise if the only x E R" so that T(x)…

A: 1.1 As T is precise, T is one-one.  Nullity of T is { 0 } i.e. dim N(T) = 0 So, by rank- nullity…

Q: Suppose T:R2 → R? is defined by T(x,y) = (x - y,x+2y) then T is %3D .a notlinear transformation .b…

A: Any transformation Tis linear transformation if and only if it satisfies the following two…

Q: Let L: R¹ R₂[r] be a linear transformation such that Lo- -1+². Calculate L 3 0 (b) x² + 5x+2 48 (a)…

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Q: Let, T: R R; 7(x, y, z) = (x- y, 2x+3y + 2z, x + y +22) Find the rank and nullity of the given…

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Q: For the linear transformation T(r,y,z)= (r-z,y+z,x+y) ker(T)= nullity(T)= : and rank(T)=

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Q: The function T: M22→R defined by T(A)=det(A) is not linear transformation. True False

A: If A is the matrix of order 2 by 2 such that the transformation: T(A)=det(A) The transformation T is…

Q: 9. Show that the function T: R³ → R3 defined by T(r, y, z) = (x – z, 2x + y, 2y – 3x) %3D is a…

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Q: Let f : R R be defined by f() = -8a Is f a linear transformation? |3D a. f(x +y) =-8x2-8y2-16ry f(z)…

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Q: 7. Show that the transformation T: R →R defined by T (x, y, z) = (x– y, 0, y + z) is a linear…

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Q: Let f : R → R be defined by f(x) -5x. Is f a linear transformation? a. f(x + y) f(x) + f(y) + Does…

A: The given function is  f(x)=-5x

Q: Let f: R R° be defined by f(x)= (-4x,7x,-3x 6). Is fa linear transformation? a. f(x + y) = f(x) +…

A: f: ℝ3→ℝ3 be defined by fx=-4x, 7x, -3x-6 (a)  fx+y=-4x+y, 7x+y, -3x+y-6⇒fx+y=-4x-4y, 7x+7y,…

Q: If T:R2 → R is a linear transformation with T and T then: T =

A: Answer

Q: Let f : R → R be defined by f((x, y)) = 2y - 5x - 4. Is f a linear transformation? a. f((x1, Y1) +…

A: The given function is                  f : ℝ2→ℝ be defined by…

Q: Let T be a linear transformation from R2 into R2 such that T(1, 2) = (1, 0) and T(−1, 1) = (0, 1).…

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Q: Suppose T:R2 → R² is defined by T(x,y) = (x - y, x+2y) then T is .a Linear transformation .b…

A: The solution is given as

Q: Find the kernel of the linear transformation.T: R3→R3, T(x, y, z) = (0, 0, 0)

A: Let T:V→W be a linear transformation. Then the set of all vectors v in V that satisfy Tv=0 is the…

Q: Let T: R3-->R4 be a linear transformation such that the only solution to T(x)=0 is the trivial…

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Q: Let T1, T2 : V → V be linear transformations satisfying Tị • T2 = ly (where 1y denotes the identity…

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Q: Let f : R → R be defined by f(x) = -9x². Is f a linear transformation? a. f(x + y) = f(x) + f(y) = +…

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Q: Let f : R → R be defined by f(x) = -3x². Is f a linear transformation? a. f(x + y) = f(x) + f(y) =…

A: linear or not

Q: Is there a linear transformation T : R → R° such that т 3 If so, what is its matrix?

A: NOTE: Refresh your page if you can't see any equations. . here we have

Q: Let f : R² → R be defined by f((x,y)) 5x + 7y. Is f a linear transformation? ((x1, Y1) + (®2, Y2)) =…

A: In the given question, concept of linear transformation is applied. Linear Transformation  A…

Q: Suppose T is the transformation from R2 to R2 that results from a reflection over the x-axis…

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Q: Suppose T: R² → R²is defined by T(x , y) = (x + y ,x ) then Tis .a Linear transformation .b…

A: