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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]

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter3: Matrices
Section3.6: Introduction To Linear Transformations
Problem 19EQ
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A = 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? random_matrix (ZZ,4,4); A 1 1 15 -9 0 0 -1 -27 [ 3 [ 0 [ 0 [ -7 -2] 1] 0] 0]
Transcribed Image Text:A = 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? random_matrix (ZZ,4,4); A 1 1 15 -9 0 0 -1 -27 [ 3 [ 0 [ 0 [ -7 -2] 1] 0] 0]
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