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3. The purpose of this exercise is to introduce a method based on the Gauss elimination method in order to extract a basis out of a gener- ating set. Begin with the vectors: 1 HOO 5 -3 Let V be the subspace of R³, spanned by these vectors. We wish to find a basis of V. All we need to do is apply the Gauss elimination method to the matrix with columns the above vectors. The columns of the resulting matrix that have a pivotal elements will correspond to the columns of the initial matrix that are linearly independent and span the same subspace as all the columns together. Apply this to the above columns and find a basis for V.

3. The purpose of this exercise is to introduce a method based on the Gauss elimination method in order to extract a basis out of a gener- ating set. Begin with the vectors: 1 HOO 5 -3 Let V be the subspace of R³, spanned by these vectors. We wish to find a basis of V. All we need to do is apply the Gauss elimination method to the matrix with columns the above vectors. The columns of the resulting matrix that have a pivotal elements will correspond to the columns of the initial matrix that are linearly independent and span the same subspace as all the columns together. Apply this to the above columns and find a basis for V.

Advanced Engineering Mathematics
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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3. The purpose of this exercise is to introduce a method based on the Gauss elimination method in order to extract a basis out of a gener- ating set. Begin with the vectors: 1 HOO 5 -3 Let V be the subspace of R³, spanned by these vectors. We wish to find a basis of V. All we need to do is apply the Gauss elimination method to the matrix with columns the above vectors. The columns of the resulting matrix that have a pivotal elements will correspond to the columns of the initial matrix that are linearly independent and span the same subspace as all the columns together. Apply this to the above columns and find a basis for V.
Transcribed Image Text:3. The purpose of this exercise is to introduce a method based on the Gauss elimination method in order to extract a basis out of a gener- ating set. Begin with the vectors: 1 HOO 5 -3 Let V be the subspace of R³, spanned by these vectors. We wish to find a basis of V. All we need to do is apply the Gauss elimination method to the matrix with columns the above vectors. The columns of the resulting matrix that have a pivotal elements will correspond to the columns of the initial matrix that are linearly independent and span the same subspace as all the columns together. Apply this to the above columns and find a basis for V.
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