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Let S = {ū, v, w}, where (2, 7, 8) v = (-16, ū = =(4, 14, 16) Consider the matrix of column vectors, A = Find its row-reduced echelon form. 56, 32) 00 Which columns have leading entries in the reduced matrix? 1 23 ū 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? v ພ 2 - 16 7-56 8 32 4 14 - 16 What is the dimension of span(S)?

Let S = {ū, v, w}, where (2, 7, 8) v = (-16, ū = =(4, 14, 16) Consider the matrix of column vectors, A = Find its row-reduced echelon form. 56, 32) 00 Which columns have leading entries in the reduced matrix? 1 23 ū 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? v ພ 2 - 16 7-56 8 32 4 14 - 16 What is the dimension of span(S)?

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, v, w}, where u = (2, 7, 8) ( 16, w (4, 14, 16) = Consider the matrix of column vectors, A = 56, 32) Find its row-reduced echelon form. v U w - 16 7 -56 32 Which columns have leading entries in the reduced matrix? 1 2 3 ∞ 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)? 4 14 - 16
Transcribed Image Text:Let S = {u, v, w}, where u = (2, 7, 8) ( 16, w (4, 14, 16) = Consider the matrix of column vectors, A = 56, 32) Find its row-reduced echelon form. v U w - 16 7 -56 32 Which columns have leading entries in the reduced matrix? 1 2 3 ∞ 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)? 4 14 - 16
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