الموضوع show that if foret A frix by and ; YーZ is a continuous map then gFo relA gf,:X b Z

Q: она горф, 123, за, 82, ха, а цу, 39,52, di, забезху на походу а ses XS a Х=1а, д, а дей робит е (9)…

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Q: Let P = (0,0, 0), Q = (1, –1, –2), R = (2,1, 1). Find the area of the triangle PQR. area = Let T =…

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Q: Show that the mogping LiPaRI-+IR L Carcaxtat = (asta, on) is liher trasfaret

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Q: Let A = the set of straight lines in the xy-plane. Let a L b mean “line a is parallel to line 6”.…

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Q: i: Let X and Y be topological spaces. Show that X Y X -Y but X -Y X - Y.

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Q: ✓1.22 Represent each linear map with respect to each pair of bases. (a) d/dx: Pn → Pn with respect…

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Q: fa) = b, Ab) = a, c) = C, 1d) = d is a one-to-one function, as each element is an image of exactly…

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Q: Let T V W be a linear map. : Show that Range T = Span{Tv₁,..., Suppose V Tvn}. = Span{V₁,..., Vn}.

A: Given : T : V→W be a linear map and  V = Spanv1, v2, ... , vn. To show : RangeT = SpanTv1, Tv2, ...…

Q: use implicit differentation t. find

A: Implicit differentiation: In an implicit differentiation, we differentiate the given equation with…

Q: 2. alsa find Levad sudfaces Tenjest plaes h pextial Deivdives Giradient

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Q: Consider the relation on R² under which two points are related if and only if they have the 2 same…

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Q: Q4. Let X = {m, n, p, q}, T = {4, X, {p}, {m, n}, {m, n, p}} and Y = {a, b, c, d}, F = {ø, X, {d},…

A: There is a slight error in the question. X cannot be an element of F. Instead of X, it will be Y.…

Q: Prove that for A # B, AB S AB S AB.

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Q: Let X be a topolegical space be a and let a Continuous map. Define the Set Y=3x€ X : flx) = x} X is…

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Q: Prove that an affine map is continuous if and only if its linear part is continuous

A: If T:A→Rk is the affine map, where A is the affine span of an affine independent subset of Rn. Let…

Q: Define a bijective map g : x2/3--->R.

A: Sol

Q: State true or false with brief justification: L1[a,b] is a reflexive space

A: We use the Theorem: Let X be a separable normed space. If the dual space X* of X is non-separable,…

Q: Q/ show thet f(2) = 2+ Conformal maps 121= 1 ? on

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Q: Let X be the set {1, 2, 3, 4, 5, 6}, Y the set {a, B, 7, 8}, and ƒ the map f(1) = a f(2)= a ƒ(3) = d…

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Q: Problem 2 Determine which of the followings are linear maps? • F: R2 → R2 given by F(x, y) = (2x +…

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Q: 1. L: V3 V4 defined by L(a, b, c) = (a - b,b+c-d, a+b-2d, b-c-d) 2. L: V4 → V3 defined by L(a, b, c,…

A: According to Bartleby guidelines we can only solve 1 question or three subparts. So put other one…

Q: if (X,d) is discrete metric space, ACX and A+D (x,d) Find the sets of A° and A (functional analysis…

A: Consider a discrete metric space X,d where d is defined as: dp,q=0,p=q1,p≠q

Q: Given F = (xyz², x²yz³, y²), find the following. (a). div (b). grad (divF) (c). curl (grad (divF))

A: We need to find the divergence of the field. F=xyz2, x2yz3, y2

Q: Does the transformation appear to be an isometry? Yes  OR no? Why OR why not?

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Q: Write a pair of curves that are homotopic and show that they are

A: it is known that two curves are said to be homotopic if one is deformed into another continuously.…

Q: Forz € C, define the linear operator T₂ : C → C by T₂(w) = W. Characterize those z for which Tz,…

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Q: A relation R on a set A is called irreflexive iff (Vx E A)((x, x) ¢ R). It is called asymmetric iff…

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Q: each comple Let t be the map se nu mber 2→X y Show that flzィ2)= fcz>fしz>).

A: Consider the given information.

Q: Let T : R3 → R² be a linear mapping. 2 .T Given that T and T find T

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Q: Let A B and g: B-C be maps. Prove that if g of is one-to-one, then / is one-to-one.

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Q: State which of the following projection functions from R? to R belong to L(IR?, R). Id1, Idı + Id2,…

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Q: 22. Let v₁ = (1, 6, 4), v₂ = (2, 4, -1), V3 = (-1, 2, 5), and W₁ = (1, -2,-5), w₂= (0, 8, 9). Use…

A: Given vectors are Here observed that So we have each of .In other words ,

Q: 4.34 (a) Prove that the composition of the projections ¹x, ¹₁: R³ → R³ is the zero map despite that…

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Q: ✓2.35 Find the nullity of this map h: Pn → R. px=1 ao + a₁x+. ....+anx¹ → ao + a₁x + + anx" dx

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