Which of the following maps is not linear? O A. L-R2-R3 defined by L(x,y) = (x+y,y.x)- OB. K:R R3 defined by K (x,y.z)=(2x,0,32) - OC f:R3-R2 defined by f (xr,y,z) = (z.x+y)- O D.TR2-R2defined by T(x.y) (x,x+y)*

Q: 4) For which one of these linear maps T:R → R? is det T > 0? a) T(1, y) = (y, -r) b) T(1, y) = (x,…

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Q: Is the map T: R² → R² given by T(x, y) = (x,y + 1) linear?

A: T: V-> W  mapping from V to W is a linear map if and only if  ->(u+v)=T(u)+T(v) ->T(au) =…

Q: (B) Prove that the stream line of b are counterclockwise circles, for that calculate F = Vx (-y ěx+…

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Q: Find the linearizations L(x, y, z) of the functions at the given points. ƒ(x, y, z) = √(x2 + y2 +…

A: Given: Function f(x,y,z) as follows: and a point (1,2,2) To find: Linearization L(x,y,z) of the…

Q: Given the map f:R→R4defined by f(x.y.z) = (0,0,0,0) then nullity of is: O A. 4 OB 2 OC1 OD.3

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Q: Let C be the line segment joining A(1,1,-2) to 0(0,0.0). A parameterization of C is given by* None…

A: NOTE : As per Bartleby guidelines only one question will be answered. Please upload other parts…

Q: In each case find the norm of the linear map L directly from the definition: (a) L : R → R with L(x)…

A: (a)  Given that the linear transformation L:ℝ→ℝ   with  Lx=-2x. The norm of the linear…

Q: Let T1: R? → R be the projection onto the first coordinate and A = {(x, y)|x > 0 or y = 0}. %3D Let…

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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: 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: Given the map f:R-R+ defined by f(x.y.z) = (0,0,x.0) then nullity of f is: O A.4 O B. 3 OCO O D-2 OE…

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Q: Let H be the plane Зx-3у+2z-0 (*) in R³, that is, H={(x, y, z)OR³ | 3x-3y+2z=0} and let F be the…

A: Given, H ={(x, y, z)∈ℝ3| 3x-3y+2z=0}Since, 3x-3y+2z=0⇒x =3y-2z3⇒H =3y-2z3, y, z∈ℝ3| 3x-3y+2z=0…

Q: Consider the linear map T : R? → R³ given by xi + x2 T (피) 4x1 where T = and the liner map S : R³ R?…

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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: 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: Given the map f:R3-R4 defined by f(x,y,z) = (0,0,0,0) then nullity of f is: OA. 3 O B. 4- OC.O O D.2…

A: For the solution of the problem follow the next step.

Q: Find the linearizations L(x, y, z) of the functions at the given points. ƒ(x, y, z) = x2 + y2 + z2…

A: given that a function f(x,y,z)=x2+y2+z2 we need to find the linearizations of f(x,y,z) at (1,1,1).…

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: 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 z = f(x, y) = x² – y² + xy + 2. Consider the triangular region in the xy-plane with corners at…

A: The given function is z=fx,y=x2-y2+xy+2

Q: x+y Let T: R3 + M,2 be the linear map defined by T y Describe ker(7) and range(T O y+z Kernel: s, t…

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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 H be the plane 2 X- 2y- z=0 in R', that is, H={(x, y, z)eR³ | 2x- 2y- z=0} and let F be the…

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Q: Let f(r, y) = |r|+ lyl- (a) Draw three r-cuts of f(r, y), three y-cuts of f(x,y), and one z-cut.…

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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: 1. Let D be the region bounded by the lines z+ y = 0, z + y = 6, z = 2y, and z = 2y – 3, and let…

A: Integrate according to the variables x,y. Find the intersection of the area bounded by all the lines…

Q: Let C be the boundaries of x2 + y² +4y 0 taken in the countercl- direction. A parameterization of C…

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Q: Let F(x, y, z) = (x-1z, y¬lz, In(xy). (a) Verify that F = V ƒ, where ƒ(x, y, z) = z In(xy). (b)…

A: Given Fx, y, z=x-1z, y-1z, lnxy (a) Verify for F=∇f where fx, y, z=z lnxy The gradient of a function…

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: Given the map f: R3→R4 defined by f(x,y,z) = (0,0,x,0) then nullity of f is: А. 0- В. 2. С. 3- O D.…

A: Given f is a function from R³ to R⁴ such that f(x,y,z)=(0,0,x,0). Let u=(x,y,z) belongs to Null(f).…

Q: (b) Let T : V → R be a linear map. If Im(T) = {0}, show that T(T) = (T, 0) where õ e V.

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Q: The domain of the function f(r, y, z) = In(6 2xy) is O {{z, y, z) E R³ ° : ay > 3} O {{z, y, 2) E R°…

A: see below the answer

Q: If L(x, y) is the local linear approximation of f(x, g(2, 1)= 4, g,(2, 1)=4 and g,(2, 1)=6, then L O…

A: Use formula of linear approximation

Q: Which of the following maps is linear? O A. None of the given maps is linear. OB. L:R2- R2 defined…

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Q: Given the map f: R-R4 defined by f(x.y.z) = (0,0.x,0) then rank of f is: A. 1. B. 4 C. 2 D.3 E. o

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Q: The domain of the function f (x, y, z) = In(6 – 3ry) is - o {(x, y) E R² : xy > 2} O {(x, y, z) E…

A: Please refer to the image below

Q: Consider the map Xn+1 = aX, (1 – X;;), %3D where a > 1. (i) Find the fixed points of the map. (ii)…

A: The function f(x) is a rule that associates or fixes a number to the particular point x. The Taylor…

Q: Given the map f: R3 R4 defined by f(x,y.z) = (0,0,x,0) then nullity of f is: O A.0 O B. 3 OCI O D.4…

A: Solution is given below

Q: Let C be the line segment joining A(1.1.-2) to 0(0.0.0). A parameterization of C is given by*…

A: The first, the third and the fifth(last) options are correct only.   The detailed solution is as…

Q: For the map F: R³ → R² defined by F(x, y, z) = (x²y + e², yz − x)

A: Given,            F(x, y, z)=x2y+ez, yz-x

Q: Let F(x, y) = <3x?y3 + y", 3x°y² + y^ + 4xy³,. %3D Evaluate F. dr where C is the line segment from…

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Q: Let H be the plane 2 X- 2 y- z=0 in R³, that is, H={(x, y, z)eR³ | 2x- zy- z=0} and let F be the…

A: Given that H=x,y,z∈R3|2x-2y-z=0 And, F(x,y,z)=2x-2y-2z2y+zy-z The aim is to find F(H).

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: (3) Suppose that T: V F is a linear map. Prove that if u E V such that u 4 Ker(T) then V = Ker(T)…

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Q: The domain of the function f (x, y, z) = In(6 – 3xy) %3D is {(x, y) E R² : xy 2} {(x, y, 2) E R³ :…

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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 &amp; S11=12 To determine: S∘T10

Q: Let L : R? → R? be the linear map defined by L(x, y) = (x + y, x – y). Show that L is invertible.…

A: Here given that L :ℝ2→ℝ2 be the linear map defined by L(x, y)=(x+y, x-y). We have to show that L is…

Q: Let X=ℝ2 and define d2,:ℝ2×ℝ2→ℝ by d2((x1 ,y1),(x2,y2)) = max{|x1 - x2|,|y1 - y2|}. a) Verify that…

A: Given that X=ℝ2 and defined by d2:ℝ2×ℝ2→ℝ Part(a): Now from given d2:ℝ2×ℝ2→ℝ by…

Q: Let F = (r-y, z+y+3, z2) and S y-direction. Compute {(r, y, z) : y =1-r²-z², y20} oriented in the…

A: Here orientation is positive y direction, surface is open.  During the calculation we ignore many…