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Linear algebra and geometry
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Let be a symmetric matrix of order with the elements of the main diagonal equal to and those on the upper and lower codiagonals equal to . Let be a matrix of order , whose th column is defined as linearly spaced elements in , . Solve the systems . The -norm of the vector is, approximately:
Evaluate for . Then, rewrite in order to avoid numerical cancellation and compute the relative error associated to , assuming as true value the one obtained with the new formulation. Approximately, its value is:
Evaluate for . Then, rewrite in order to avoid numerical cancellation and compute the relative error associated to , assuming as true value the one obtained with the new formulation. Approximately, its value is:
Let us take the matrix ; find the right statement:
Let us consider the matrix and let be the characteristic polynomial of the matrix . Find the right statement.
The points from the parametric line satisfy the equations
Which one of the following statements is true?