(3) Consider the weighted graph G: a b d g h Weights for G: f Edge Weight Edge Weight Edge Weight ab 2 cd 14 eg 12 ad 8 се 13 ei 12 ае 10 cf 16 fg 1 af 5 de 11 fh 15 bc 15 dg 6 fi 7 bd 9 dh 17 gh 19 bf 4 di 2 hi 20 ef 18 Use Kruskal's algorithm to find a minimal connector and state its weight.

3. Can you think of a connected graph with four vertices, so that the span of the columns of the adjacency matrix is R¹? Can you generalize this to a graph with n vertices?

. Use the simplex algorithm to solve the following linear optimisation problem: maximise f(x1, x2, x3) = 3x1 + x2+ 2x3 subject to: Зх1 + 2л2 + з 0.

Given a graph G = (V,E) find the minimum number of edges that will cover every vertex (Edge Cover). Detail and analyze an approximate algorithm to this problem.

Find the shortest path from vertex 'S' to 'T’ by Dijkstra's algorithm for the weighted graph: 3 3 d 1 4

O Classkick H Video Conferencing, Meetings x di (7) Meeting in "General" ( x X Edgenuity-Student Learning x A app.classkick.com/#/account/student-works/AXkoclamT0aHg4WrnXIVYw/questions/AXkOAebiQluanAQj9YYmTg arks USATestprep, LLC - 88 25. (4/26) Unit 4 Practice Test --/1 Pt 18/33 Find the measure of the angle indicated. 100° 110 ° 114° Sign o acer 41 6 7 85

obtain the least squares fit for a line

Dijkstra algorithm is an algorithm for finding the shortest paths between nodes in a weightedgraph. Given a graph and a source vertex in the graph, find shortest paths from source vertex (B) to allvertices in the graph below.

4. A slightly easier spline interpolation is the so-called quadratic spline. Interpolation is carried out by piecewise quadratics. What are the suitable joint conditions for quadratic spline? Show how the coefficients of this spline are obtained. • What are the suitable end conditions? • Compare the required computational efforts for quadratic and cubic spline. 1 • Write a Python code for interpolating the Runge function f(x): at equi-spaced nodes using a quadratic spline. 1+25x²

Find maximum and minimum value with langranfe multiplier