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3 cards from this section. Quick, good the night before a test.
What is a system of linear equations?
Think about what characterizes a linear equation.
Write the matrix form of the equations: x + 2y = 5 and 3x - y = 4.
Recall how to form matrices from equations.
What does LU decomposition achieve?
Remember what LU stands for in this context.
True or False: The Gauss-Jacobi method always converges for any matrix.
Consider the conditions for convergence we discussed.
Given the matrix A = [[4, -2, 1], [1, 1, -1], [-1, 2, 5]] and vector B = [3, 1, 0], use Gaussian elimination to find the solution.
Keep track of your row operations carefully.
Consider a large sparse matrix derived from a real-world dataset. Discuss when you would prefer to use Gauss-Seidel over direct methods and justify your choice.
Reflect on the characteristics of sparse matrices.
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