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In Exercises 7-11, use the technique of Example 2, described in the box on page 129, to find a basis for the subspace spanned by the given vectors. 7. sp([−3, 1], [6, 4]) in R² 9. sp([2, 1], [−6, −3], [1, 4]) in R²

In Exercises 7-11, use the technique of Example 2, described in the box on page 129, to find a basis for the subspace spanned by the given vectors. 7. sp([−3, 1], [6, 4]) in R² 9. sp([2, 1], [−6, −3], [1, 4]) in R²

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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In Exercises 7-11, use the technique of Example 2, described in the box on page 129, to find a basis for the subspace spanned by the given vectors. 7. sp([-3, 1], [6, 4]) in R² 9. sp([2, 1], [−6, −3], [1, 4]) in R²
Transcribed Image Text:In Exercises 7-11, use the technique of Example 2, described in the box on page 129, to find a basis for the subspace spanned by the given vectors. 7. sp([-3, 1], [6, 4]) in R² 9. sp([2, 1], [−6, −3], [1, 4]) in R²
Finding a Basis for W = sp(w₁, W2, ..., Wk) 1. Form the matrix A whose jth column vector is w,. 2. Row-reduce A to row-echelon form H. 3. The set of all w; such that the jth column of H contains a pivot is a basis for W.
Transcribed Image Text:Finding a Basis for W = sp(w₁, W2, ..., Wk) 1. Form the matrix A whose jth column vector is w,. 2. Row-reduce A to row-echelon form H. 3. The set of all w; such that the jth column of H contains a pivot is a basis for W.
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