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Let S = {ū, v, w}, where ū u = (4,4, (4, 4, — 7) v = ( - 20, 20, 35) w = (12, 12, — 21) - Consider the matrix of column vectors, A = 4 4 -7 - 20 - 20 35 12 12 - 21

Let S = {ū, v, w}, where ū u = (4,4, (4, 4, — 7) v = ( - 20, 20, 35) w = (12, 12, — 21) - Consider the matrix of column vectors, A = 4 4 -7 - 20 - 20 35 12 12 - 21

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 = (4, 4, 7) v (- 20, W - 20, 35) (12, 12, -21) Consider the matrix of column vectors, A = Find its row-reduced echelon form. 4 4 -7 Which columns have leading entries in the reduced matrix? 1 2 3 What is the dimension of - 20 - 20 35 span(S)? 12 12 - 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? -21
Transcribed Image Text:Let S = {u, v, w}, where u = (4, 4, 7) v (- 20, W - 20, 35) (12, 12, -21) Consider the matrix of column vectors, A = Find its row-reduced echelon form. 4 4 -7 Which columns have leading entries in the reduced matrix? 1 2 3 What is the dimension of - 20 - 20 35 span(S)? 12 12 - 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? -21
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