Consider the following system of linear equations to answer the below questions: 6x₁ + 7x₂ + 2x3 = 5 7x₁ + 5x₂ + 4x3 = 0 X₁ + 7x3 = 5 a) Determine the dominant eigenvalue and the dominant eigenvector using three iterations of the power method. b) Use the method of deflation to construct the matrix in which its dominant eigenvalue is the second eigenvalue of the above system based on the answer of part 'a'. c) Determine the determinant of the matrix of the coefficient using LU- decomposition

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