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
Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter7: Eigenvalues And Eigenvectors
Section7.CM: Cumulative Review
Problem 25CM: Find a basis B for R3 such that the matrix for the linear transformation T:R3R3,...
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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](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb8d8cfad-e835-4d24-9d1e-941fcbe41049%2F600fcfc2-d3e5-4984-ad77-9faddc10783e%2Ffnli5lk_processed.png&w=3840&q=75)
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
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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