Given a linear map L:R-R such that L(1,0,0)=(3,-1),L(0,1,0)=(2,1),L(0,0,1)=(3,0) , then find L(1,-2,3) ? a. (8,-3) b. (5,2) c. (-1,3) d. (3,-3)

Q: Let T: R2 - R3 be the linear map which satisfies and 3 Give the formula for T. x + 3y x + y

A: We have to find

Q: (3) Consider the linear map T : R? → R² which sends (1,0) → (-3,5) and (0, 1) → (4, – 1). (d) What…

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Q: Which of the following sets is linearly independent? M={(1,3,4), (1,2, 5), (- 1 ,0,-2)} O M-((1,…

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Q: Find (a) the image of v and (b) the preimage of w for the linear transformation.T: R3→R3, T(v1, v2,…

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Q: If the range of the linear transformation T :R° → R' is R³ then the nullity of T is a) 2 b) 3 c) 4…

A: Rank-Nullity theorem: Let  T : V→W be a linear transformation, with V a finite-dimensional vector…

Q: Which of the following maps T, L, I, f: R³ → R³ is not linear? a) 1(x, y, z) = (x, y, z). b) f(x, y,…

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Q: If (x, y) → (x +3, y- 7)maps TUVWto T'U'V'W', what is the algebraic description that will map…

A: Consider the given: Mapping TUVW to T'U'V'W':x,y→x+3,y-7 Find the algebraic description that will…

Q: Given the transformations, which one is linear?   (a) T: R2 → R3, T(x, y) = (x - y, 3x - 2y) (b) T:…

A: Consider a transformation T :ℝn → ℝm is Linear if(i)  T(u+v)=T(u) +T(v)(ii) T(αu)  =αT(u) for all…

Q: Which of the following maps from R³ to R³ are not linear? f(x, y, z)=(x, y, z + 1). f(x, y, z) =…

A: The function f is said to be linear if: f(X+Y)=f(X)+f(Y)f(kX)=kf(X) where X,Y∈ℝ3.

Q: (b) h: M2x2 → IR given by b Ha + d d (c) h: M2x2 → P2 given by (: )- H a+ b+c+ dx² (d) the zero map…

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Q: 4. Consider two maps S,T: R" R". The composition So T is a linear map if and only if both S and T…

A: 4. Consider two maps S,T:IRn→IRnThe composition SoT is a linear map ifboth S and T are linear maps

Q: Which of the following points are coplanar? a. (-4, 1, 0), (0, 1, 2), (4, 3,-1), and (0,0, 1) b.…

A: set of points are given, we have to find coplanar points

Q: Which of the following maps from R³ to R³ are not linear? U □ f(x, y, z)=(x, y, z + 1). f(x, y, z) =…

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Q: a b L:M,(R)→R’, L 2)-(a+26,b-3c,c+d)

A: First I have written the definition of Linear Transformation , just use this definition for given…

Q: a) Is there exists a linear map T: R² → R² for which T(7,7) = (4,-5) and T(2,2) = (8,-2)? Justify…

A: As per our guidelines, we are supposed to solve only first subpart. Kindly repost other subpart as…

Q: Let f: R² → R³ be a linear map such that f(1,2)=(1,1,2), and f(2, 1) = (2,2,1). Then which equalitie…

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Q: Given the transformations, which one is linear?   (a) T: R2 → R, T(x, y) = | x | (b) T: R2 → R2,…

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Q: 2. - For each map below, either prove that it is linear or demonstrate that it is not linear. (a) T…

A: Consider a map T:U→V is linear if    (i) T(u+v) =T(u)+T(v)   (ii) T(αu )   = αT(u)   , for all u,v…

Q: Let : R³ → R¹ be a linear map such that /(1,2)=(1,1,2), and /(2, 1) = (2,2,1). Then which equalitie…

A: Let V(F) and W(F) be two vector spaces over field F and f:V→W be a linear map. Then, a)…

Q: Find fy, fy, and f, and evaluate each at the given point. ху fx, у, 2) (8, 1, –1) x + y + z f,(x, y,…

A: We know that the division rule of partial derivative , If f ( x , y , z ) = h ( x , y , z ) / g ( x…

Q: Find f, f, and f, and evaluate each at the given point. f(x, y, z) = x²y + 2xyz - 8yz, (-3, 1, 3)…

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Q: If (x, y) → (x + 3, y - 7)maps TUVWto T'U'V'W', what is the algebraic description that will map…

A: Given x,y→x+3,y-7 maps TUVW to T'U'V'W'. Let (x,y)→(a,b) where a=x+3, b=y-7 x=a-3,y=b+7 Therefore,…

Q: ent, find a linear relation. a) vi = (2, 1, 0), V2 = (0, 1,0), V3 = (-1,2,0) %3D b) wi = (1,2, –2),…

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Q: Which of the following maps is not linear? А. T:R²→R² defined by T(x,y) = (x²2,x+y)· В. f:R3→R2…

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Q: Let f: R2 R³ be a linear map such that f(1,2)= (1,1,2), and f(2, 1) = (2,2,1) which equalitie are…

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Q: Find (a) the image of v and (b) the preimage of w for the linear transformation.T: R2→R2, T(v1, v2)…

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Q: State if the following statement is true or false. The map p4 p 3 defined by (xv,z,w)=( w,z x, x+ y)…

A: Solution is given as below:

Q: Let T: R -→ R° be linear map such that T(1, y, z, w) = (y – 2x, y + w, z), then ker T A) {(t, 2t,…

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Q: Let F(r, y, z) = (y+ z²) i+ (x² – y)j+(z² – x) k, and let C be the piecewise-linear path from (1,…

A: answer  D correct option

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: :R3-R3 defined by  T(x,y,z)=(x,y,0) Show that T is linear and find its range and kennel

A: T : IR3→IR3 defined asT (x,y,z) = (x,y,0)Let (x1,y1,z1) , (x2,y2,z2) ←IR3 and ⋉←IR ThenT…

Q: Given the map f:R4 3 defined by f(x,y,Z,w) = (0,0,0) Then rank of , is: f O A. 1 O B. 3 OC.O O D.2 O…

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Q: Let T: R2 R be a linear map such that T(x, y) = (2x, 3y, 2y- r), then one of the following in range…

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Q: Let be a linear map such that L(3,0,1) = (2,7,11) and L(1,0,0) = (1,2,4)· Then the value of L(4.0.2)…

A: A detailed solution is given below

Q: Given the map f:R3 R4 defined by f(x,y,z) = (0,0,0,0) then rank of f is:

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Q: : R³ → R², find its dual map, where (i) 1(x, y, z)=(x-y, y+z), (ii) t(x, y, z) = (x + y + 2z, 2x+y),…

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Q: Let f: R2 R³ be a linear map such that f(1,2)= (1,1,2), and f(2, 1) = (2,2,1). Then which equalitie…

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Q: Let f: R2 R³ be a linear map such that ƒ(1, 2) = (1,1,2), and ƒ(2, 1) = (2,2,1). Then which…

A: We are given that f is a linear map such that f(1,2)=(1,1,2) and f(2,1)=(2,2,1)

Q: is any linear map, then the foll Im f¹ = (Ker (f))º Ker (f¹) = (Im f)⁰ T0

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Q: Let: R² R³ be a linear map such that /(1,2)=(1,1,2), and /(2,1)=(2,2,1). Then which equalitie are…

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Q: Determine whether each of the following maps from R? to R³ is linear. Prove your answers. (a) F((x,…

A: Let V(F) and V'(F) be vector spaces.  T: V(F)→V'(F) is said to be linear transformation if…

Q: Find f, fy, and f,, and evaluate each at the given point. z' fix, y, 2) %3D х*уз + 2хyz - 8yz, (-3,…

A: We will do partial differentiation.

Q: Consider the linear map T: M, ,- R° defined by 2a+b a b c d 2c+d Find either the nullity or the rank…

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Q: Select all of the transformations that would result in the perimeter of a triangle being the same as…

A: Note: According to Bartleby guidelines for more than one question asked; only the first one is to be…

Q: For any linear map f: EE, lez D). If f2 = id, then /1

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Q: Find F, and f, and evaluate each at the given point. fx, y, z) - xy + 2xyz - Syz, (-2, 1, 2) ,G Y.…

A: topic - partial differentiation

Q: Which of the following maps from R³ to R³ are not linear? 0 f(x, y, z)=(x, y, z + 1). f(x, y, z) =…

A: The solution is given below

Q: 4. Consider two maps S, T: R" R". The composition So T is a linear map if and only if both S and T…

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Q: Let T : R? →→ R² and S : R² → R² be a linear maps such that r() - (1) (G) = (;) TO and S(( 2 1 Then…

A: Given: T: R2→R2 ,  S: R2→R2 be linear maps such that T10=11 & S11=12 To determine: S∘T10

Q: O Let f: R2 R³ be a linear map such that f(1,2)= (1,1,2), and f(2, 1) = (2,2,1). Then which…

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