Regarding the criterion used to decide on the plane that best ts a set of data points in k + 1 dimensions:a. What is that criterion called?b. Specically, what is the criterion?

Q: 3. Show that the set W = {(x, 0) : x e R} is a subspace of R?.

A: In order to show W is a subspace of R2 , we need to prove W is closed under addition. For any two…

Q: 5. Write a rule for the translation of a point of the plane figure above. A. (x,y)→ (x-2,y+3) B.…

A: Translation of a point of the plane means moving all the points of that plane to a new coordinate.

Q: 12 3. 5. 13 18 -1 For what value of hs in the plane spanned by j and i? Preview Answers Submit…

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Q: Find the distance between the given pair of points in Exercises 25–28. 25. (−1, 4, −3) and (−4, 3,…

A: To find the distance between the pair of points given: d=x2-x12+y2-y12 in a two coordinate plane.…

Q: Use a least-squares fit to find the plane of best fit through the points (x;, Y;, Z;) E {(1,2, 1),…

A: In this question, we find the equation of best fit of the plane by least squares method, Given that…

Q: Determine the Miller indices of a plane that makes intercepts of (4, 3 and 8) on the coordinate axes…

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Q: Determine the Miller indices of the plane that passes through three points having the following…

A: Given,     (a) (0, 0, 1); (1, 0, 0); and (1/2, 1/2, 0)  (b) (1/2, 0, 1); (1/2,0, 0); and (0, 1, 0)…

Q: snip

A: The given equation is the parabolic equation                    y = x2

Q: 4) Show that the subspaces of R? are precisely {0}, R2, and all lines in R? through the origin.

A: A subspace of a vector space is itself a vector space that is contained in another vector space.

Q: Draw a figure that shows the image of the triangle with vertices (0, 0), (1, 0), and (1/2, 1) under…

A: It is given that the vertices of the triangle are 0, 0, 1, 0 and 12, 1. We have to sketch the graph…

Q: Estimate the parameter a for the set D using MLE.

A: MLE is known as the maximum likelihood estimator .It is widely used in the field of estimation and…

Q: 1.Find the area of the triangle in the xy-plane with vertices A(n,,n2, n2),B(m,,m2,m3),C(r,,r2, 13).

A: Please see the explanation below

Q: 3. Consider a plane going through the point p -1 and with normal n = 4 Write down an algebraic…

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Q: Determine the image of the upper half plane {z € C : Im(z) > 0 }

A: In this question, we use the transformation under g(z) we find the image set.

Q: 9. Is Y = {(x,y, z) | y=z} R?? a subspace of

A: ψ={(x,y,z)| y=z}

Q: Bounded by the coordinate planes and the plane 3x + 2y + z = 6

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Q: Determine the Eq.  of plane (M) pass through points A(0,2,0), B(1,1,1), C(-1,0,2)

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Q: 3. Decide whether the following statement is TRUE or FALSE. If TRUE, give a short explanation. If…

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Q: Use Lagrange multipliers to find the points on the given cone that are closest to the following…

A: Let (x,y,z) be the point which is closest to the point (2,4,0) .

Q: 4) Let x be the twor diminsional spore cquipped with the scolor product. ke subspace Yis gitn by the…

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Q: Consider the foilowing. Ax3y Sketch a graph of the plane.

A: The solution of above question is written below.

Q: Consider the design given by the general finite projective plane P2 (F,), where p is a prime number.…

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Q: Let-{ », :x, y, a, b e R and x - a = y – b}.Is W a subspace?

A: We will use the one step test for vector subspace to check if W is a subspace or not. We know that…

Q: Theorem 4.23. Let A be a closed subset of a normal space X. Then A is normal when given the relative…

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Q: What is the norm of a partition of a closed interval?

A: Concept: The calculus helps in understanding the changes between values that are related by a…

Q: ---- Let a, = |4|, a, = 3 and let b = |1, for what value of h is b in the plane spanned by a, and…

A: Given that a1=145,  a2=238   and  b=11h. This implies that, xa1+ya2=bx145+y238=11hx+2y=1…

Q: 2. Find a unitvedctor with positive z-component porpendcular to the plane 2xt2y-2=3 Z-C

A: We will find out the required value.

Q: Find the distance between the planes. 5x-2y+z-4 0, 5x-2y+z+6= 0

A: Given,  Equation of Plane 1: 5x - 2y + z - 4 = 0 Equation of Plane 2: 5x - 2y +z + 6 = 0 From the…

Q: 5. Evaluate 2XZds where S is the part of the plane - 2x +4+Z =3 over the triangle with bounds…

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Q: Find all planes in R3 whose intersection with the xy-plane is the liner( t) = t ( 2, 1, 0) .

A: GIVEN  Intersection with the xy-plane is the line r( t) = t ( 2, 1, 0)

Q: Use Green's theorem to calculate where C is the rectangle with vertices (0, 0), (2, 0), (2, 3), (0,…

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Q: If V is infinite-dimensional and S-is an infinite-dimensional subspace, must the dimension of V/S be…

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Q: A tessellation is a collection of two-dimensional figures that fit together to cover a plane or part…

A: True

Q: The point (-2,0,8) is. A. In die xy-vlak O In the xy-plane B. In die yz-vlak O In the yz-plane C. In…

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Q: Find the equations of the tanget plane and normal line to the graph of In(2?)x-을=3y3-VE at the point…

A: Equation of tangent plane f(x, y, z) = k at x0, y0, z0 is, fxx0, y0, z0x-x0+fyx0, y0, z0y-y0+fzx0,…

Q: Let P(V) be a projective space of dimension > 2, and let [v], [v2), [v3] € non-colinear points…

A: A common definition of "projective plane" includes the following axioms: every pair of distinct…

Q: What is the Boundedness Theorem?

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Q: Given a Vector space V, if S is to be shown to be a subspace of V, is it enough to show that the…

A: Given a Vector space V, if S is to be shown to be a subspace of V, is it enough to show that the…

Q: A cube of cheese from Italy with edge measure of 1 was cut by Mickey using a plane in a manner that…

A: Let us assume the the cordinates OA= OB= OC= 1

Q: Use Lagrange Multiplier to find the Point P (x,y,z) closest to the origin on the plane containing…

A: The equation of the plane passing through the three points can be obtained using the matrices. The…

Q: Find the minimum distance from the point (8, 3, 4) to the plane x - y + z = 4. (Hint: To simplify…

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Q: are subspaces of R ?

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Q: Find the general equation of the plane passing through P(−1, 3, −2) and having n = (−2, 1, −1) as a…

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Q: Find the coordinates of the point Y that lies 2. along the directed line segment from X(-1,3) to…

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Q: Use Green's Theorem to evaluate $. xydx + x²y³dy, where C is the triangle with vertices (0,0), (1,0)…

A: Consider the provided question, ∮cxydx+x2y3dy,     where c is the triangle with vertices 0,0, 1,0…

Q: The pyramid is bounded below by the xy plane above by the plane x+y+z=3 and on the sides by the xz-…

A: According to the given information it is required to set the double integral to find the volume of…

Q: How many points and lines does a finite projective plane of order 7 have?

A: The number of points in a projective plane of order n is n2+n+1. The number of lines in a projective…

Q: The set W consisting of all the points in R? of the form (x, x) is a straight line. Is W a subspace…

A: Given that the set W consisting of all the points in R2 of the form of (x, x) is a straight line.

Q: 2 Let w = z². Find the image of the first quadrant in z-plane

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