Question

a) Answer the following: i) Construct a 2x2 system of equations that has a unique solution and briefly explain your rationale. Solve the system using the AX=B matrix method. Note

that all coefficients must be non-zero. ii) What are the possible values of the parameters a, b such that the following system of equations has no solutions? Give one specific possible pair. Briefly explain your solution. 3x – ay = b -bx + 4y = -3 b) Answer the following: i) Solve the following system of equations, using Gauss or Gauss-Jordan elimination ONLY. 4x - 2у+ 2z = 0 5х + у - z = 0 -X - 3y + 3z = 0 ii) Find two bases for the spanning set of (u, v, w), where u = (4, 5, -1), v= (-2, 1, -3) and w =(2, -1, 3). c) You have a small collection of 4 pdfs and you have just calculated all possible similarities using the cosine coefficient. You found that: - D1, D3 and D4 have nothing in common with each other. D2 and D3 are plagiarised identical copies. D1 and D2 are 50% similar to each other. D2 and D4 are 25% similar to each other. Give the 4 x 4 similarity matrix for this scenario and provide a brief explanation for your solution.

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