Given any two Euclidean spaces E and F, w ension m, for any linear map ƒ: E→F, we have Ker f = Ker (f* of), Ker f*=Ker (foƒ*), Ker f = (Im f*), Ker ƒ* = (Im ƒ)¹, 17. 14.

Q: p+q Consider the function f(p, q, r) = w = 2. af with p = v²w³ + u, q = w³ + v², and r = uv³ + 1.…

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Q: +++++ ++ + 2 riecononi ni bilw no elV us led (Jq 1) () ++++ dordw go alnoji vas da 1 (1g 1) (b) YOe…

A: follow next step

Q: 1. Let V, W be finite-dimensional vector spaces. Define the map from L(V, W) to L(W', V') by $(T)=T…

A: Given that V and W are finite dimensional vector spaces. Let dim V=m and dim W=n. Then we can write…

Q: Let X {1,2, 3} and Y {3,4}. Define f : X → Y as follows: = f(2) = 3 and f(3) = 4. Draw an arrow…

A: We will draw the arrow diagram for function mapping from set A to set B.

Q: The relation on Z × N defined by, (a, b) ~ (c, d) if ad bc.

A: The objective is to show that the relation a,b~c,d then ad=bc is an equivalence relation. To show…

Q: Suppose that L1 is the line through point (1, 2, 3) with direction vector [2 ,- 3 ,0]t. And suppose…

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Q: Figure 4 shows the contour map of a function f (x, y) together with a path r(t) in the…

A: Given, the contour map of a function f (x, y) together with a path r(t) in the counterclockwise…

Q: 21. Let f(x) = 2x, x = [0, 1]. Take P = {0, 1, 1, 1, 1, 1} and set x₁=1, x₂ = 16, x3 = 3, x4={, x3 =…

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Q: Let f function from (R,d ) to (R,d1) defined as d(x) = x , where d discrete metric and d1 .is the…

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Q: 2. (a) Let ds² = v du² − du dv + 2 dv². (a) Find the largest subset U of R² for which this…

A: (a) Given metric:ds2=v du2−du dv+2 dv2Comparing g11=v , g12=g21=−12 , g22=2Given metric will be…

Q: Let f function from (R,d1) to (R,d2) defined as d(x) = x, where d, is the usual metric and d2 is the…

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Q: Let f: R R be the absolute value function and let g : R → R be an affine map for which g(0) = 0.…

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Q: Translate the image by the directed line segment from (0,0) to (4,1).

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Q: Consider the following mappings on RXR: * d1(1, y) = e²=y, d2 = |2r - 2y). and d3 = V12r – yl. %3D…

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Q: 12 10 1. Estimate 30 20 10 ƒ(6,4).

A: Given: Contour map of nice function, To estimate: f6, 4

Q: Consider the following mappings on RXR: d1(x,y) = e*-Y, d2(x,y) = |2x –yl and d3(x,y) V=yl O Both d1…

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Q: given that z is a function of x and y which satisfies xyz+exyz=2, find ∂z/∂y using implicit…

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Q: Sketch the space curve. Vector-Valued Function r(t) = -ti + 5tj + 2tk O Z -2 XX k k Z 5 5 5 2 2…

A: Given Data: rt=-ti+5tj+2tk   0,1 To Find the length of the given interval.

Q: 4. Show whether or not f is bijective. Letf : R → R_be defined as f(x) = I피+1 %3D

A: A function f is said to bijective if it is one-one and onto

Q: If possible, determine the vector, parametric,symmetrical and reduced line r that: a) passes…

A: Given the lines S1:t·1,2,3, t∈ℝ and S2:y=x+2, z=x. To find a line L passing through the point P1,1,1…

Q: tch the following contour diagrams (cross-sections to the z-axis) to the following fund II) IV) 0.5…

A: Given contour diagrams and their functions. The objective is to match the contour diagrams with…

Q: 1.T.2 Let V be the set of all twice-differentiable functions f : R → R satisfying f"(x) = f(x) – 5.…

A: Let, f and g be two functions in V.  Then,        f"(x) = f(x) - 5       g"(x) = g(x) - 5.

Q: Let f : [a, b] → R be a two-to-one map, i.e., for every y E Im(f), there are exactly two points a1,…

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Q: Let F = Vf and f = 5x²y - 5z. Calculate F. dr for the path r₁ = (t, t,0), 0 ≤ t ≤ 1. (Give your…

A: We will use fundamental theorem of line integrals

Q: 2) The contour map of f(x, y) is shown below. Use it to find fx (1,3) 10 10 8 8 6 =2 6 0 x=2 6 8 10

A: fx​(1,3)=1   Explanation:From the given contour map, we can see that, f(1,3)=4  Similarly we can…

Q: 8. let C be the curue space ret) = (e*,2et ,2et ),0s ts lnca) the rength of C is

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Q: Let 7,V be a projection af the Vect or space. Accordling to this: Show that every Xe Im (T) for…

A: The given problem is related with projection. Given that T is a projection of the vector space V .…

Q: For each of the following, determine (with argument) whether the given function T is linear. 1. The…

A: To identify which of the given function is linear transformation.

Q: Consider the following mappings on RXR: * d1(x, y) = e2z-y, d2 = |2x – 2y|, and d3 = VI2x – y|. %3D…

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Q: A. Show that T is a topology in X and Show that B,(x) is open set with respect to t for all r > 0

A: This is a problem of Topology.

Q: 6) The contour map of a function C(x, y) is shown below. Use it to answer the following questions.…

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Q: A contour map is shown for a function f on the square R= [0,8] x [0,8]. Assume a = 4, b = 8, c = 4,…

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Q: Let F: RP → RP be a differentiable map. Given u, v ERP, show that Du+vF = D₂F + D₂F.

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Q: Match the space curves in the figure below with the following vector-valued functions: O A. r(t) =…

A: See that options ,  A )  r ( t ) = < 1 , t , t >  If we consider the first two coordinates ,…

Q: A For each of the following maps T: V→ W, find the spaces V and W and say if they are linear or not…

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Q: of the following statements I. Let f and g be continuous real variable functions defined over the…

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Q: Let f: R R be the absolute value function and let g : R -→ R be an affine map for which g(0) = 0.…

A: Given f:ℝ→ℝ is the absolute value function, that is,                  fx=x, for all x∈ℝ and g:ℝ→ℝ is…