4. Find a translation that maps A(2, –3) onto B(4,–2).

Q: Let a = (5, 5, - 3) and b = ( – 5, 3, 0). Find the projection of b onto a. proj¡ b = <

A:

Q: Let z= y- 4a, a u'v and y-v- 3u. Compute On kum)-(1,1) -

A:

Q: 10. Prove that T, is topologically conjugate to the quadratic map F(z) = 4z(1 - z).

A: Solution of 10. To prove that T2 is topologically conjugate to the quadratic map F4, we have to find…

Q: 02 Define a Map L: M232M.3 by 1 3. LHA)-1 A, Is L a L2 lincar transformotion? Pove yovy AssertionB

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Q: 2.4 (Ross, 2003, page 593) Show that the relationship $ (x) = x;¢(1;, x) + (1 – x;)ø(0¡, x) is true…

A:

Q: b) Is there a linear map T: V → W, where dim V = 3, dim W = 4, rank T = 2, and dim ker T = 1?

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Q: Let →a=⟨3,1⟩ and →b=⟨1,0⟩. Find the projection of →b onto →a. proj→a →b=

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Q: 2. Given: PT || QS Prove: APRT O AQRS a. R. b. What similarity transformation maps APRT onto AQRS?

A:

Q: 4. Describe the reflection(s) that will carry the rectangle onto itself. 10 -10-9 -7 01 -2 -6

A: Given: The rectangle ABCD. To describe: The reflection of rectangle.

Q: find the Zero and order of the Linear trans formation TIRR defined as Teab)=la+bg d-byb)

A:

Q: 7. i) Show that Q(2'4,i)/Q is a Galois extension.

A: The given function is, E=ℚ214,ii,e, E=ℚ24,i The minimal polynomial of 24 is  x=24Taking power 4 both…

Q: o Show that X2 = {(x, y) E X x X : x<y} is a sublattice of X x X. %3D

A: Given that X is a lattice. To show that X[2]  is a sub lattice of X×X. It is enough to show that,…

Q: Suppose N E L(C) is nilpotent and has a Jordan form with only one Jordan block. Describe a Jordan…

A: According to the given information,

Q: Suppose that the translation T is described by (?,?)→(?+2,?−1)(x,y)→(x+2,y−1). What translation…

A: We have to find the translation described in x,y→x+2,y-1.

Q: 9. Show that the function (-, -) : IR² × R² → IR defined by setting = #1#2 + 2x12 + 2y1*2 + 8y1Y2 /2…

A:

Q: Let Myn2 defined by TCA) =A+A". Fünd bases for Ker GT) and Range CT).

A:

Q: o Show that X2 = {(x, y) € X × X : x < y} is a sublattice of X x X.

A: Given that X is lattice Given that X[2] The objective is to show that X[2] is a sublattice of X×X.…

Q: Let a = (- 4, 5) and b = (4, – 3). Find the projection of b onto a.

A:

Q: Suppose that a linear transförmation / satisfies T(u,) = T(u,) = -1 -2 Find T(4u, - 3u,). T(4u, -…

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Q: (d) Compute the cross product (0, 2, 1) × (1, 3, 1).

A:

Q: Q3: Prove that ,X; = y %3D %3D are symmetries of 31'4 12 113

A: Given: To prove that are symmetries of

Q: The orthogonal projection of y onto u is the same as the orthogonal projection of y onto cu whenever…

A: solution

Q: Evaluate the Jacoblain Jlu,v, w) for the transformatión : X = VW , y= Ww %3D

A:

Q: Let a = ( – 3, 4) and b = ( – 3, 1). %3D | %3D Find the projection of b onto a. projā b %3D

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Q: (b) Use part (a) to show that f (T) is either a transposition disjoint transpositions. or a product…

A:

Q: Let a = (4, 1) and b = (2, – 2). Find the projection of b onto a. proja

A: We have to find projection of b→ onto a→ for given vectors a→=4,1 and b→=2,-2 We know the projection…

Q: Which of the following points are collinear to (1,0) and (3,6)? Show graphically and analytically.…

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Q: Find a norm for C([0, 1]), so that C([0, 1]) is not complete under this norm.

A:

Q: 10 What are the coordinates of the point on the directed line segment from K(-5,-4) to L(5, 1) that…

A: Use mid section formula for evaluating the coordinates of points.

Q: -5 1 Let y = -2 U2 = = In 4 -1 Compute the distance d from y to the plane in R spanned by uj and u2.…

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Q: Prove that the Joukowski map 1 p(2) : (z + maps ONTO T - (-1, 1)

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Q: If Ea, is divergent and 2b, is divergent, then E(a, + ba) is divergent.

A: Taking an example and than we are trying to understand tha statement.

Q: 4 Let y = U2 = -7 U1 = -4 4 -6 -2 -9 Compute the distance d from y to the plane in IR° spanned by u̟…

A:

Q: 10 What are the coordinates of the point on the directed line segment from K(-5,-4) to L(5, 1) that…

A: We have to find out coordinates

Q: 2 Given u -1 and U , for which w is the set {u, v, w} linearly independent?

A:

Q: Suppose T E L(U,V) and S € L(V, W) are both invertible linear maps. Prove that ST E L(U, W) is…

A: First we prove that ST is a invertible linear map from U to W and then it will be shown that the…

Q: If a translation maps zH onto LJ, which of the following statements is true?

A: First, we must perform the analysis of the diagram:   1. By translating angle H to angle J,…

Q: 3. (a) Show that under the mapping w = 1/z, all circles and straight lines in the =-plane are…

A: (a) We have to show under the mapping w = 1/z, all circles and straight lines in the z plane are…

Q: Let →a=⟨5,−4⟩ and →b=⟨4,3⟩ Find the projection of →b onto →a proj→a →b

A:

Q: Consider the map S: M2,2 → M22 defined by S(A) = AA.

A: Consider the map S(A): M2,2→M2,2ByS(A)=AATo check S(A) is linear transform.

Q: at x and y are orthogonal

A: Given: x and y in ℝn, x+y=x-y To show:  x and y are orthogonal in ℝn if and only if x + y = x − y

Q: What are the perpendicular generators on (P) to 4 %3D of the surface

A: Given equation s are, x216-y24=z....1x3=y2=z-4...2 Equation of generators of the hyperboloid (1) are…

Q: 3 O (x, y) → (y,x) t (^ 'x-) (x) O (x-X-) (x) O O (x,y) → (x, -y)

A: Let's solve.

Q: Let a = (– 1, 5, 0) and b = (3,0, – 1). Find the component of b onto a.

A:

Q: 3.2.21. Draw a connected path starting at (0,0) that, if continued, would pass through all of Z ×Z.

A: The connected path is a continuous mapping in which a continuous image is formed. In other words,…

Q: Let a = (4, 0, – 5) and b = (- 2, 5, 2). Find the projection of b onto ä. proją b

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Q: Let a = (- 3, – 5) and b {1, 2). Find the projection of b onto a. proj; b = >

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Q: Let à = (1, − 1, — 5) and 6 = ( – 5,0,− 1). Find the projection of b onto a. proj¡ b = >

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Q: Let ä = (4, – 4, 0) and b = (- 1, 2, - 4). Find the projection of b onto a. proj, b = <

A: