Exercise 1 - Nearest Neighbors 2D for binary classification: We are given the following training examples in ((-3,5), +), ((-4, –2), +), ((2,1), -), ((4,3),–) Assume that we want to classify the points (-2,0) and (-1,5) using (a) . .a 1-nearest neighbor rule, and (b) a 3-nearest neighbor rule. Use the Euclidean distance (L2-norm) for calculating the distance between the points, in order to determine the k nearest neighbors to the query points given. What is the classification of these two points in each case?

Q: Draw the directed graph of the relation R = {(1,2), (2,1), (1,1), (2,2), (3,3), (4,1)} X=123 43

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Q: Consider the relations R = {(1,5), (2, 2), C S%3D { (2,4), (3, 4), С T3 {(1,4), (3, 5), С on the set…

A: The solution is given below.

Q: 3. Describe span S if: a) S= {(1,1); (2 ,6); (7,12)} b) S= {(1,0,2); (3,2, –7); (–1,–2,11)} c) S=…

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Q: Let A, = {..., – 2,- 1,0,1,...,i}. Find

A: Ai={..., -2, -1, 0, 1, ......, i} ∩i=1nAi=?

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A: Use the definition of composition of functions to solve this problem as in next step.

Q: In (Z24, €) find the orders of the elements 3, 4, 6, 7, and 18.

A: Hey, since there are multiple questions posted, we will answer the first question. If you want any…

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Q: Illustrate the key ideas in the proof of Hall's Matching Theorem.

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Q: Example 68: (R, +,.) and (Q.+,.) are fieleds. (H.W)

A: I have proved the definition of field

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Q: Verify the relations (5).

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Q: Consider an interpolating polynomial p(x) of degree ≤ 3 satisfying p(xo) = a, p'(xo) = b, p(x₁) = c…

A: Since you have posted a question with multiple sub-parts, we will solve the first three sub-parts…

Q: y QI:: Let X₁, X₂ ~ N(0,1) 1) X1-X₂ X₁ + X2 2) (x1+x²)2 X₁-X2 what dist of 2X² 3) x² + x²

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A: R-code for the above problem is given as below: w= seq(from= 1, to= 29, by = 2)ww_remove <-…

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Q: Explain whny the following binary relation on. 1,2,3} Is not R=…

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