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Let u = = [−6, −18, 6], v = [−4, -9, 10], and w = [4, 8, -12]. We want to determine if the set {u, v, w} is linearly independent or dependent. Construct the matrix A = [ whose rows are the three given vectors, and then reduce it to row echelon form using only three elementary row operations: First add Then add Finally add u times the first row to the second (in order to eliminate the leading entry of row two). times the first row to the third (in order to eliminate the leading entry of row three). times the new second row to the new third row (in order to eliminate the new leading entry of row three). From the reduced matrix, we conclude that: A. the set {u, v, w}| is linearly dependent O B. the set {u, v, w} is linearly independent C. we cannot tell if the set {u, v, w} is linearly independent or not

Let u = = [−6, −18, 6], v = [−4, -9, 10], and w = [4, 8, -12]. We want to determine if the set {u, v, w} is linearly independent or dependent. Construct the matrix A = [ whose rows are the three given vectors, and then reduce it to row echelon form using only three elementary row operations: First add Then add Finally add u times the first row to the second (in order to eliminate the leading entry of row two). times the first row to the third (in order to eliminate the leading entry of row three). times the new second row to the new third row (in order to eliminate the new leading entry of row three). From the reduced matrix, we conclude that: A. the set {u, v, w}| is linearly dependent O B. the set {u, v, w} is linearly independent C. we cannot tell if the set {u, v, w} is linearly independent or not

Algebra and Trigonometry (6th Edition)
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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Let u = [−6, −18, 6], v = [−4, −9, 10]|, and w = and w = [4,8, -12]. We want to determine if the set {u, v, w}| is linearly independent or dependent. u 9 V whose rows are the three given vectors, and then reduce it to row echelon form using only three elementary row W Construct the matrix A = operations: First add Then add Finally add times the first row to the second (in order to eliminate the leading entry of row two). times the first row to the third (in order to eliminate the leading entry of row three). times the new second row to the new third row (in order to eliminate the new leading entry of row three). From the reduced matrix, we conclude that: A. the set {u, V, w} is linearly dependent B. the set {u, v, w} is linearly independent C. we cannot tell if the set {u, v, w} is linearly independent or not
Transcribed Image Text:Let u = [−6, −18, 6], v = [−4, −9, 10]|, and w = and w = [4,8, -12]. We want to determine if the set {u, v, w}| is linearly independent or dependent. u 9 V whose rows are the three given vectors, and then reduce it to row echelon form using only three elementary row W Construct the matrix A = operations: First add Then add Finally add times the first row to the second (in order to eliminate the leading entry of row two). times the first row to the third (in order to eliminate the leading entry of row three). times the new second row to the new third row (in order to eliminate the new leading entry of row three). From the reduced matrix, we conclude that: A. the set {u, V, w} is linearly dependent B. the set {u, v, w} is linearly independent C. we cannot tell if the set {u, v, w} is linearly independent or not
Expert Solution
Step 1: Define the problem

Let u equals open square brackets negative 6 comma negative 18 comma 6 close square brackets space comma space v equals open square brackets negative 4 comma negative 9 comma 10 close square brackets space comma space w equals open square brackets 4 comma 8 comma negative 12 close square brackets

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