Look back at the matrix A. Can you spot a dependency amongst its rows? While it is possible to find matrices where there is a dependency among the rows (or columns), such matrices are rather rare. If you create a random matrix, it's rather likely that it will have no such dependencies -- and will therefore be invertible. There are multiple ways to create random matrices in sage. Try executing the following cell to get a random 4 x 4 matrix, then find it's inverse using the augmentation/row reduction process. How can you spot whether you got unlucky and ran into a non-invertible matrix? A = random_matrix (ZZ,4,4); A 1 15 -9 0 0 -1 -27 [ 3 [ 0 [ 0 [-7 1 -2] 1] 0] 0]

Look back at the matrix A. Can you spot a dependency amongst its rows? While it is possible to find matrices where there is a dependency among the rows (or columns), such matrices are rather rare. If you create a random matrix, it's rather likely that it will have no such dependencies -- and will therefore be invertible. There are multiple ways to create random matrices in sage. Try executing the following cell to get a random 4 x 4 matrix, then find it's inverse using the augmentation/row reduction process. How can you spot whether you got unlucky and ran into a non-invertible matrix? A = random_matrix (ZZ,4,4); A 1 15 -9 0 0 -1 -27 [ 3 [ 0 [ 0 [-7 1 -2] 1] 0] 0]

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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