Let f : R → R³ be defined by f(x) = (-9x, –2x, –5x). Is ƒ 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? b. f(cæ) = c(f(x)) = Does f(cx) = c(f(x)) for all c, æ E R? c. Is fa linear transformation? +

Q: Let 3 = {1, x, x²}, and consider the linear transformation T : P2 (R) → P2 (R) defined by Тр(x)) —…

A: Given transformation is T(p(x))=3p(x)+2p'(x) Given basis is β={1,x,x2}…

Q: Let T: P2 → P1 be the linear transformation defined by d T(ax² + bx + c) = (ax² + bx + c). dx T(4x²…

A:

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

A:

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: If T : R' → R', T(x) = Ax is a linear transformation that maps onto R', then Ax = 0 has only the…

A:

Q: If T: R³ → R³ is a linear transformation such that (E) (B) T T T (E) then T = 4

A: Given that T : ℝ3→ℝ3 is a linear transformation such that           T100=334, T010=-1-30, T001=-14-4

Q: (b) Prove that the mapping T:R2 → R³ from R² into R³, defined by T(x, y) = (x + 1,2y, x + y) is not…

A: A mapping T is a linear transformation if and only if a) T(x+y) = T(x)+T(y) b) T(ax) = aT(x)

Q: Show that the function D : Vn(I) → Vn(I) defined by D(x(t))=x′(t) is a linear transformation.

A:

Q: [8] Find the inverse of the linear transformation T: R³ → R³ given by Z - T|y| = [x +y]

A: We will use knowledge of basic linear algebra to solve this.

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 f : R² → R be defined by f((x, y)) = 9x – 9y – 5. Is f a linear transformation? a. f(("1, Y1)…

A: Given : f :ℝ2→ℝ is defined by          fx, y=9x-9y-5 To determine if f is a linear transformation or…

Q: Let f : R? → R be defined by f((x,y)) = 8y – 2x. Is f a linear transformation? a. f({®1, Y1) + (x2,…

A: The objective of the question is examine the linear transformation.

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

A:

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

A:

Q: Let f : R? → R be defined by f((x, y)) = 8y – 5x + 8. Is f a linear transformation? a. f(x1, Y1) +…

A:

Q: Let f : R? → R be defined by f((r, y)) = -8x – 5y. Is fa linear transformation? a. f(r1, Y1) + (x2,…

A:

Q: Given the function T:R²→R³ defined as X2 2x2 – X1 4x1 | i) Show that T is a linear transformation.

A: To show that T is linear transformation, where:

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

A:

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

A:

Q: Let f : R → R° be defined by f(x) = (-2x, 7x, 7x). Is ƒ a linear transformation? a f(r + y) f(r)+…

A:

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: Let T: R³ R³, T(x, y, z) = (8x + 7z, y, 9x + 8z) be an invertible linear transformation. The inverse…

A:

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

A:

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

A:

Q: Let f : R? → R be defined by f((x, y)) = 9x – 7y. Is f a linear transformation? a. f((r1, Y1) + (x2,…

A: It is given that the function f : ℝ2→ℝ is defined by fx, y=9x-7y. We have to check whether f is a…

Q: 2. Let T: R R defined by T1 – 12 + 13 -r +3r2-2.r3 T2 T3 Prove that T is a linear transformation.

A: we have to the following transformation is a linear transformation

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: T(xy)=Cax?+by?, cx²+dy²) 2

A:

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,…

A:

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: Suppose that T : R" → R" is a linear transformation with T(u) = v and T(v) T(4u – 2v) in terms of u…

A: A linear transformation T is a transformation which is linear in the vectors. It follows the…

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)…

A:

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…

A:

Q: Find the null-space of the linear transformation from R3 to R² given by: (1 A = 2 \1 2 3/ 1

A: We have to find the null-space of the linear transformation from ℝ3 to ℝ2 given by A = 112123

Q: Let f : R → R be defined by f((x, y)) = 9x + 6y. Is ƒ a linear transformation? a. f((r1, Y1) + (x2,…

A:

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)…

A:

Q: Let B = {1, 1+ x, x + x² } and y = {1, x, x² }, and consider the linear transformation T:P2 (R) → P2…

A: We have to find Matrix T with respect to Basis B and r.

Q: Let f : R → R* be defined by f(x) = (x, -8x2, 6x). Is f a linear transformation? a. f(x + y) f(x) +…

A:

Q: Let T(x) = Ax be a linear transformation, andA is as follows: -5 4 1 -6 Is T onto R2? а. Yes b. No

A: According to question given that 1-5401-6

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^3 be defined by f(x)=⟨6x,−4x,−4x⟩⟩. Is f a linear transformation?  (a) f(x+y)=f(x+y)=(?)…

A: We have to find the following conditions according to the given information

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

A:

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

A:

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: 4. Let L: R→ R' be the linear transformation defined by Find L

A: