Let Pe B(H) be a nonzero orthogonal projection. Show that |P| = 1. %3D

Q: Find the image of the circle |Z – 2| < 2 in the z – plane under the inverse transformation w = by…

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Q: Does the following function satisfies the symmetry condition? a(v, u) = f(vxK Ux +vAu)dx -1

A: Given,        a(v, u)=∫-11(vxκux+vλu)dx

Q: In Exercises 5-12, let G(u, v) = (2u + v, 5u + 3v) be a map from the uv-plane to the xy-plane.…

A: Describe the image of the line through the points (u, v) = (1, 1) and (u, v) = (1, -1) under G in…

Q: 2. Let x = (1, 1, 1, 1)" and y = (8, 2, 2, 0)". (a) Determine the angle 0 between x and y. (b) Find…

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

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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: Construct a linear map L(z)=az+b that will send the imaginary y-axis to the line v=-u.

A: we have to constract a linear map that maps the y-axis to the line v=-u Basically we have to…

Q: Prove that if V = W ⊕W⊥ and T is the projection on W along W⊥, then T = T∗. Hint: Recall that N(T) =…

A: V = W ⊕W⊥ and T is the projection on W along W⊥To show: T = T*Recall that N(T) = W⊥, R(T) = W

Q: Find the eigenvalues and eigenvectors of A geometrically.

A: Given,   Find the eigenvalues and eigenvectors of A,   where   A=162512251225925

Q: (G) G)- The projection of onto the line through zero 1 is and а. (;) () " () b. C. d.

A: Let u→=11, and the line l through zero v→=00, and w→=1-1. Need to find the projection of u→ onto the…

Q: 1. Let u= (0, -2,3), v= (1,4, 1). Evaluate a) the projection proju(v) of v over u And b) the area of…

A: Given: Let u= (0,-2,3)   and  v=(1,4,1) To find a) the proju(v)  of u over v b) area of the…

Q: Let E The orthogonal projection of y on H = span{ u 1, ú 2} is given by:

A: Given

Q: 4. Evaluate . F.ds , where C is the triangle with vertices (1,0,0), (0,2,0), and (0,0,3) oriented by…

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Q: Every linear transformation x = au + bv, y = cu + dv with ad – bc + 0 maps lines of the uv-plane…

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Q: nd the orthogonal trajectories of the family of confocal central conics given as: = 1 a² + à b² + à

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Q: Let a = (- 3, 4) and b = (- 3, 1). Find the projection of b ont a. proja b

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Q: Q1) Use a suitable Linearization to find the best fit of the form f(x) = Cx3 + for the %3D data:…

A: Given the data,                 (1, -1), (2, 7), (3, 26.3)

Q: 2: Show that a map T is linear if and only if T(Au + v) = XT(u)+ T(v) for all A ER and vectors u, v.

A: A linear transformation satisfies  T:U-V  Then T(u+v) = T(u) +T(v)          T(au) = aT(u)  For all a…

Q: Let G(u, v) - (8u + v, 5u + 5v) be a map from the uv-plane to the xy-plane. Calculate Jac(G).

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Q: et D be a parallelogram with vertices (0,0), (= nd a linear transformation x-x(u,v), y-y(u,v)a (x…

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Q: Compute the Jacobian of the map G(r, s) = (er cosh(s), er sinh(s))

A: The given function is G(r, s) = (er cosh(s), er sinh(s)). Compute the Jacobian as follows.

Q: Find the orthogonal projection of y onto u. - 8 4 y = u: 6. 12 O A. 1 4 3 4 О В. 4 12 Ос. 16 48 O D.…

A: We have to find orthogonal projection of y on u.

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 the transformation u = 2x – y, v = x + 3y to find p (2x-y)3 dA, x+3y where R is the…

A: .

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

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Q: tnd the kes reetor projection of anto r if

A: Given : u→=5i→+2j→ and v→=6i→-3j→

Q: . Calculate the projection of å along b and projection of b along å when: d = 3î + j – k , 5 = -21 –…

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Q: 9. f(z) = e'm/4 z %3D

A: Given: Triangle  with vertices 0,1 ,i . f(z) =eiπ4 z To find:  image of given triangle under f(z)

Q: 6. Let y = 9 , U1 , U2 1 |3| L10] 1 Compute the orthogonal projection of y onto W = Span{u1, u2}.…

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Q: Suppose three non-collinear points in R have non-zero position Vectors a, B, Consider a linear…

A: The three non-collinear points in R3 have non-zero position vectors a,b,cT:R3→R3 satisfying…

Q: Use the coordinate transformation u = x + 2y, v = x - 2y to evaluate S (x2 - 4y)dA over the…

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Q: Use the given transformation to evaluate the integral. (12x + 12y) dA, where R is the parallelogram…

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Q: Let a→=⟨-2,0,1⟩ and b→=⟨-5,5,-2⟩. Find the projection of b→ onto a→.

A: Given two vectors a= (-2,0,1)  and b=(-5,5,-2) The scalar projection of b⇀ onto a⇀ is given by…

Q: Set up a transformation and hence evaluate R over the rectangular region enclosed by the lines * + y…

A: Transformation means change of variables in multiple integrals.  We transform the integral using…

Q: 4. let f(x, y) = x² – xy + y² – y. find the direction u and Duf at Po(1,–1) for which Duf is the…

A: Given:- f(x, y) = x2 -xy+y2 -y To find:- Direction u and Du f at point p0 (1, -1) for which Du f is…

Q: The function f : R? → R given by f(x, y) = x² + 2y is a linear transformation. O True O False

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Q: 3. Show your work. Simplify your results. -{()}-- () and b= Let L = Span (b) (c) Find the matrix P…

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Q: In R', evaluate the alternating 2-form 5 = -3 · dx ^ dy on the pair of vectors (a, b) If %3D a = (4,…

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Q: Let G(u, v) = (5u + v, 3u + 3v) be a map from the uv-plane to the xy-plane. Calculate Jac(G).

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Q: Give Z(G), the center of G, for G = S3 %3D

A: Definition of Center: Let G be a group. The set of all elements which commute with every other…

Q: Let v = and v3 1 for which values of S, v,, V2 , and v3 are linearly %3D V2= %3D indonondont

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Q: onto y %3D Find the projection of I =

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Q: Exercise 4.1. Let F : R² → R² be the map defined by F (;) = () for any () E R². Describe the image…

A: Let ab∈R2 If ab satisfies x2+y2=1 then, 2a3b satisfies the equation x22+y32=1.

Q: Find the image of the set S under the given transformation. S is the square bounded by the lines u =…

A: S is the given square bounded by the lines u=0, u=1, v=0, v=1 and transformation x=v and y=u(1+v2)…

Q: Find the image of the circle |Z – 2| < 2 in the z– plane under the inverse transformation w = by…

A: Question (7)

Q: (1, 2, 1) on to the line x = 2+ t, y = 3 – t, z = t. Also Find Find the Projection of b = Projection…

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Q: Fit a linear function of the form f(t) = co +ct to the data points (-2, –14), (0, 10), (2, 22),…

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Q: (f) Find the length of the projection of i onto ū.

A: Given

Unitary Method

The word “unitary” comes from the word “unit”, which means a single and complete entity. In this method, we find the value of a unit product from the given number of products, and then we solve for the other number of products. 

Speed, Time, and Distance

Imagine you and 3 of your friends are planning to go to the playground at 6 in the evening. Your house is one mile away from the playground and one of your friends named Jim must start at 5 pm to reach the playground by walk. The other two friends are 3 miles away.

Profit and Loss

The amount earned or lost on the sale of one or more items is referred to as the profit or loss on that item.

Units and Measurements

Measurements and comparisons are the foundation of science and engineering. We, therefore, need rules that tell us how things are measured and compared. For these measurements and comparisons, we perform certain experiments, and we will need the experiments to set up the devices.