Let R' have the Euclidean inner product and let u = (1, 2, –1) and v = (3, 1, 0). Then proj u

Q: Determine a scalar s such that A2x = sx when Ax = rx.

A: To determine a scalar s such that A2x=sx when Ax=rx Given Ax=rx On multiplying both the sides by…

Q: Find the divergence of the vector field F <7", 22°, zy* div F -

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Q: Evaluate the Jacobian of G(u, v) = (u3 + v, uv) at (u, v) = (2, 1).

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Q: Let C be the positively oriented square with vertices (0,0), (2,0), (2,2), (0,2). Use Green's…

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Q: .

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Q: Define the weighted Euclidean inner product on R', (u, v) = u1v1/3+4u2v2. Calculate ((-) () 2

A: NOTE: Refresh your page if you can't see any equations. . so here we have

Q: Show that (x, y) = 5x1y1 – 9x2y2 for vectors x = (x1, x2) and y = (y1, y2) in R2 defines an inner…

A: This question is about application of linear algebra

Q: Prove that if {y1,...,yn} is an orthogonal set of nonzero vectors, then the vectors {x1,...,xn}…

A: Let consider the orthonormal set of nonzero vector be {w1, w2 …wn} instead of {y1...,yn} and the…

Q: Find the divergence of the vector field F(x, y,z) = x²zi – 2xzj + yzk and the point (2, -1, 3).

A: Divergence of a vector field: The divergence of a vector field F = (P, Q, R) is given by, The given…

Q: Consider the vector space Rn with inner product{x, y} = xTy. Show that for any n × n matrix A,(a)…

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Q: . Show that (x, y) = 4x1y1 – 7x2y2 for vectors x = (x1, x2) and y = (y1 y2) in R2 defines an inner…

A: Given two vectors x and y in R2. We need to show that the given function in x and y defines an inner…

Q: Consider the set of vectors S = {(1, 0, 0), (0, 1, 0)} and the field F = R of real numbers, then…

A: The given set  of vectors S=1,0,0,0,1,0

Q: Find the divergence of the vector field F→(x,y,z)=xyzi→−yzj→+xzk→at the point (8,3,2) .   Enter…

A: The given vector field is : Fx,y,z=xyzi-yzj+xzk To find the divergence at 8,3,2

Q: Let (V, (,)) be an inner product space and let f, g be vectors in V. If || F|| = 4. ||g|| = 5 and ||…

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Q: Let (V, (, )) be an inner product space and let v, w be vectors in V. If (v, w) = 7 and w = 5, then…

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Q: Let u = (x²yz, ry z, ryz?). Compute curl i

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Q: Let f(x) = sin x and  g(x) = sin x + cos x  in the vector space C, [0, 2π] with the inner product…

A: Given that, f(x) = sin x and  g(x) = sin x + cos x Consider an inner product in them for f , g C ∈…

Q: Consider the vector space 2 with the inner product rgk)=x+1,then %3D

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Q: Use the inner product (f, 9) = | f(x)g(x) dr %3D in the vector space CU[0, 1] of continuous…

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Q: Find vector x and y in R? that are orthonormal with respect to the inner product (u, v) = 4u1v1…

A: Let x=14,0, y= 12,0 Hence, by using the given inner product, we have x,y=414(0)…

Q: Use the inner product (f,9) = f(z)g(x) dz in the vector space C"0, 1] of continuous functions on the…

A: It is given that fx=-5x2-3 and gx=9x-7. We have to evaluate f, g, f, g and αf, g where αf, g is the…

Q: Show that the functions o,(x) = sin(nax²), for n = 1,2,3,..., form are orthogonal set with respect…

A: Consider the equation

Q: Compute the flux of the vector field (x, (æ°, – ay*), out of the rectangle with vertices (0,0),…

A: To compute the flux of the vector field x3,-xy4, out of the rectanglewith vertices 0,0,2,0,2,4…

Q: Show that V={(x,2020x): x in R} is a vector space

A: According to the given information, it is required to show that the given set is a vector space.

Q: Find work done by a force field F= in moving object along the line segment from the point (2,1,3) to…

A: Given, F=1y-x,xyz,ex2+y2+z2

Q: True or False: (p, q) = pq defines an inner product on P(R).

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Q: Justify that (•, ·) defines an inner product on R?. the function (', ·) defined on R? as follows: U1…

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Q: Is = xjx + yjy+zźz3 an inner product on R'?

A: No it is not an inner product.  Inner product looks like a dot product.

Q: Sketch the vector field on given byF(x, y, z )= z K

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Q: Find the level surfaces of the scalar field U = ear, where the vectors are: a = (2, 2, 1) and r = =…

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Q: 10. Show that V = R² with the standard scalar multiplication, but addition defined by (7, , v.) +…

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Q: 4. Show that the norm on l0 given by I| (11, .., In...) |lo= sup{|r;| : j= 1,2, ...} can not be…

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Q: Consider R' endowed with the dot product. Let W = span{u1, u2} where u1 = (1,0, 1) and u2 = (-1, 1,…

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Q: Determine a scalar s such that A2 x = sx when Ax = r x.

A: Given that Ax=rx. Multiply both sides of the above equation by A and simplify as follows.

Q: Show that the function does not define an inner product on R3, where u = (u1, u2, u3) and v = (v1,…

A: For satisfying the inner product condition, function has to follow these three conditions: 1)…

Q: Let R' have the Euclidean inner product and let u = (1,-2,-1) and v = (3, 1,0) Then proj, u %3D

A: AS PER GUIDELINES I HAVE SOLVE ONLY FIRST ONE

Q: Suppose {u, v, w} is an orthonormal set in R". Prove that u +v is not orthogonal to v + w.

A: The set {u, v, w} is an orthonormal set. Therefore, the modulus of each vector is 1. The vectors u,…

Q: Find the curl of the vectòr field F(x, y, z) = 2xyzi + 8yzj + 5zk

A: According to our guidelines we are supposed to do only one question.  Kindly repost other question…

Q: Find the orthogonal projection of f onto g. Use the inner product in C[a, b] (f, g) = f(x)g(x) dx.…

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Q: Show that the function defines an inner product on R3, where u = (u1, u2, u3) and v = (v1, v2,…

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Q: Let (V, (, )) be an inner product space and let v, W be vectors in V. If (v, w) : = 7 and |w| = 5,…

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Q: Let i = (x²yz, ry z, zyz?). Compute curl i

A: The given vector is: u→=x2yz, xy2z, xyz2

Q: Find (u, v), ||u|l, ||v||, and d(u, v) for the given inner product defined on R". u = (-4, 0), v =…

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Q: 3. Show that the vector field F = -C with C> 0, is conservative and find its potential.

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Q: Find (u, v), ||u|, |v |, and d(u, v) for the given inner product defined on R". u = (-5, 4), v = (0,…

A: We have given vectors u and v,  And we have to find a), b), c) , d)

Q: Find (u, v), ||u||, ||v||, and d(u, v) for the given inner product defined on R". u = (-5, –12), v=…

A: For the given inner product

Q: Show that the function defines an inner product on R2, where u = (u1, u2) and v = (v1, v2). ⟨u, v⟩ =…

A: Given function u,v=u1v1+9u2v2 where u=u1,u2 and v=v1,v2 The function is defined on R2. To show that…

Q: 2. Verify that the usual length of Vector in the has the plane properties in 3 dinensional Space…

A: Given: usual length of a vector in the plane or in 3 dimensional. To prove that this vector has the…

Q: Find (u, v), ||u||, ||||, and d(u, v) for the given inner product defined on R". u = (-5, -12), v =…

A: a) Given,  u= ( -5, -12)  v = (-15, 8)  We have to find &lt; u, v &gt; We know,  &lt;u, v&gt; = dot…

Contingency Table

A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.

Binomial Distribution

Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.