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Let S = {u, v, w}, where u = ( − 1, 2, 1) v = = (11, - 22,5) =(2, 4, 2) Consider the matrix of column vectors, A = Find its row-reduced echelon form. Which columns have leading entries in the reduced matrix? 1 2 3 ■ ū -1 2 1 201 11 - 22 5 We want to reduce S to a linearly independent set with the same span. That is, we will use a subset of S to form a basis for span(S). Based on the row-reduced echelon form of A, identify which vectors should be used to form this basis? What is the dimension of span(S)? - 2 4 - 2

Let S = {u, v, w}, where u = ( − 1, 2, 1) v = = (11, - 22,5) =(2, 4, 2) Consider the matrix of column vectors, A = Find its row-reduced echelon form. Which columns have leading entries in the reduced matrix? 1 2 3 ■ ū -1 2 1 201 11 - 22 5 We want to reduce S to a linearly independent set with the same span. That is, we will use a subset of S to form a basis for span(S). Based on the row-reduced echelon form of A, identify which vectors should be used to form this basis? What is the dimension of span(S)? - 2 4 - 2

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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Let S = u = (1, 2, 1) v = {u, v, w}, where (11, - 22,5) w=(2, 4, 2) Consider the matrix of column vectors, A = Find its row-reduced echelon form. - ū 21 Which columns have leading entries in the reduced matrix? 1 2 3 ■ w -1 2 1 We want to reduce S to a linearly independent set with the same span. That is, we will use a subset of S to form a basis for span(S). Based on the row-reduced echelon form of A, identify which vectors should be used to form this basis? 11 - 22 5 What is the dimension of span(S)? - 2 4
Transcribed Image Text:Let S = u = (1, 2, 1) v = {u, v, w}, where (11, - 22,5) w=(2, 4, 2) Consider the matrix of column vectors, A = Find its row-reduced echelon form. - ū 21 Which columns have leading entries in the reduced matrix? 1 2 3 ■ w -1 2 1 We want to reduce S to a linearly independent set with the same span. That is, we will use a subset of S to form a basis for span(S). Based on the row-reduced echelon form of A, identify which vectors should be used to form this basis? 11 - 22 5 What is the dimension of span(S)? - 2 4
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