A) compute x the component of x that is parallel to L and x the component of x that is orthogonal to L B) compute the reflection of x across the line L; refL(x)

Q: Prove that the three points (;q, yx), (x2, y2), and (x3, y3) are collinear (lie on the same line) if…

A: Given : The three points are : x1, y1, x2, y2 and x3, y3 Now we have to prove that  x1, y1, x2, y2…

Q: Consider j1,ỹ2, ỹ,ER° and that ỹ,+y;+ÿ;=0. For Î=span{ÿ, ,ÿ and Y=span{ÿ2, ÿ}, show that Ý=Ỹ.

A: Given y1→, y2→, y3→∈ℝ5 such that y1→+y2→+y3→=0. Let Y^=spany1→,y2→ and Y~=spany2→,y3→. To show…

Q: Draw the bifurcation diagram for i = (x – 3)(c+ x)

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Q: (2,3) is te i చాంబ! Under a ro dediona Identidy three distinct point that Cald be the center & of

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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: (c) Compute the distance in AU between the points (x,0) = (1.24,0) and (1.24, 7)

A: Given: The coordinate transformation, x=Rsinhχsinθcosϕ y=Rsinhχsinθsinϕ z=Rcoshχcosθ The plane…

Q: Since Cov (X, Y) = E [X, Y] -E [X] E [Y]. Obtain Cov (Yi, BO)

A: From the given information, Consider, the regression equation be assumed as given below:…

Q: Parametrize the directed line segment which joins the point −2 + 3i to the point 5 − 7i, that is,…

A: The parametric equation on a line passing through the points x1,y1 and x2,y2 is given as follows:…

Q: 6. Prove that (i) the three points A(1,4,2), B(3, 2, 4) and C(5,0,6) are collinear, (ii) the four…

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Q: { (0,3), (0,1) is linearly independent in R? ylgn O Ins

A: The given vectors are  (0, 3) and (0, 1) To find whether they are linearly dependent or not

Q: Let F = cos(5t) i+ 3tj+ 5t° k and G = ° cos(5t) i +²j+5e* k Find the cross product Fx G =

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Q: Sketch z =- 2cos y in R3

A: The expression y=cos(x) will give the graph of a cosine curve in the x-y plane, with the value of y…

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).

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Q: Which of the following would be a line of reflection that would map ABCD onto itself? 3 B 2 D Ox=1…

A: For the solution follow the next steps.

Q: Let v = (3, 0, 0) and w = (0, 1, −1). Determine u = v × w usingthe geometric properties of the cross…

A: Cross product: more formally called the vector product a way of multiplying two vectors and produces…

Q: 1. Construct the bisector of XY.

A: We need to draw bisector of line. AS per our guidelines we can not solve multiple questions so I am…

Q: Consider the following. u = −7i - 2j - 4k, V = 4j + 4k (a) Find the projection of u onto v.

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Q: 4. Classify and reduce the following equations to a canonical form: (a) yu -x*u, = 0, x>0, y>0. (b)…

A: To classify and reduced in canonical form of the given equation is..

Q: Prove that H(x, y) = (x, –y) provides a conjugacy between x' = (4 })x and Y'= (; 7). X and Y' = 1 -1…

A: Given: X' =11-11XY' =1-111Y To prove: H(x,y) = (x , -y) provides conjugacy between both of the above…

Q: (1 point) If a = i +j+ 3k and b =i+j+2k Compute the cross product a x b. axb 0 i+0 01

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Q: In AEFG, L is the centroid. If LJ=9 find EL. H J E K

A: We have given a triangle. In which LJ is the centroid. And we have to find EL

Q: 1. Let a = (1, 1, –1) and b = (2,4, 6). Find the cross product a x b and verify that it orthogonal…

A: Given: a=1, 1, -1b=2, 4, 6 To Find:  To find the cross product a×b, and, to verify that it is…

Q: Suppose NOL -> QRM is a reflection across the x-axis. If O(9, 4) what is the y coordinate of R?

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Q: Show that if PER"×" is an orthogonal projector, then P+ = P.

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Q: Use Cramer's rule to solve for y without solving for the un- knowns x, z, and w. 4x + y + z+ w= 6 3x…

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Q: Consider, 21u = 2x – 3y and 21v = -–x+y Find the value of the Jacobian a (x, y) a (u, v)

A: 21 u = 2x - 3y, 21 v = -x + y

Q: Find the projection of b = 5i – k onto à = i+ 2j+ 3k. %3D

A: We have to find the projection of →b on →a

Q: Consider the Simple Linear Model: 4 = Bo + Biz, + e, where i = 1,...,n, and e ~ IID(0, o?). Suppose…

A: Simple linear regression model: A simple linear regression model is given as y = b0 + bx, where y is…

Q: 18) (Section 9.7) Find the cross product in space u = 3i – 2 j+4k v=i-3j-k

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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 = 4i + 3j – k, b = 2i – j + xk and c = yi + zj – 2k. Find: %3D %3D a x such that a and b are…

A: Two vectors are said to be perpendicular to each other if their dot product is zero. We will use…

Q: Find the harmonic conjugate of u where u(x,y)=x^2 - y^2 -2xy-2x+3y

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Q: Let P, Q, and R be the points at 1 on the x-axis, 2 on the y-axis, and 3 on the z-axis,…

A: Let O is the initial point (0, 0, 0) and the vector OP, OQ and OR vector can be represented as:

Q: Suppose vi, v2, ..., m is linearly independent in V and w ɛ V. Show that v1, vz, ..., Um, W is…

A: v1, v2,......., vm is linearly independent in V and w∈V

Q: Draw the bifurcation diagram for i = (x – 3)(c + x)

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Q: Find the image of |z + pi + 2p| = 4 under the mapping w = p√² (e¹²) z. about

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Q: Current Attempt in Progress Let a = ci +jandb = 9i + 45j. Find c so that a and bare orthogonal. c =…

A: Given :a=ci+j and b=9i+45jTo find : The value of c so that a and b are orthogonal.

Q: Find the angle between x and x4 in C[0,1] with its standard inner product.

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Q: Let V =(1,2,3,4),V=(0,2,t,3) and w=(!,!,,1) 1. Find t so that u t v and w are to each other. or…

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Q: Complex Analysis

A: For given function, First we will show the function is harmonic function as shown below :From the…

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: Compute the Jacobian of the mapping. G(r, t) = (2re", 3 + 8e")

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Q: 3 Find the e qu.of Plane that Contains elol; 3) and Parallel to the X-2 Plane and PerPendicular to…

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Q: If a = i + j + 5k and b = i + j + 3k, compute the cross product aXb

A: We have to find cross product

Q: Prove the following property of the cross product: u X kv = k(u X v)

A: Let u=u1 i+u2 j+u3 k  &  v=v1 i+v2 j+v3 k. Then, kv=kv1 i+kv2 j+kv3 k Now,…

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: Find the image of | z – 3i | = 3 under the mapping W =-.

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Q: 6. Prove that (i) the three points A(1, 4, 2), B(3,2,4) and C(5, 0,6) are collinear, (ii) the four…

A: Given: i) A(1, 4, 2), B(3, 2, 4) and C(5, 0, 6) ii) P(2, -1, 1), Q(1, 3, -2), R(-2, 1, -3), and S(3,…

Q: Suppose NOL -> QRM is a reflection across the x-axis. If O(1, 9) what is the y coordinate of R?

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