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BL I be a r IX. a. What is the maximum number of pivot positions M can have? 7 Answer the rest of the questions assuming M has less than the maximum number of pivot b. Are the rows of M linearly independent? O No Yes ONeed more information (could be either) c. Are the columns of M linearly independent? O No Yes ONeed more information (could be either) d. How many solutions does Mv = 0 have? Zero One

BL I be a r IX. a. What is the maximum number of pivot positions M can have? 7 Answer the rest of the questions assuming M has less than the maximum number of pivot b. Are the rows of M linearly independent? O No Yes ONeed more information (could be either) c. Are the columns of M linearly independent? O No Yes ONeed more information (could be either) d. How many solutions does Mv = 0 have? Zero One

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 M be a 7 x 7 matrix. a. What is the maximum number of pivot positions M can have? 7 Answer the rest of the questions assuming M has less than the maximum number of pivots. b. Are the rows of M linearly independent? No Yes O Need more information (could be either) c. Are the columns of M linearly independent? No Yes Need more information (could be either) d. How many solutions does Mv 0 have? Zero One = X Infinitely many Need more information (could be more than one of these) X e. How many solutions does Mv = b have for each b? Zero One Infinitely many Need more information (could be more than one of these)
Transcribed Image Text:Let M be a 7 x 7 matrix. a. What is the maximum number of pivot positions M can have? 7 Answer the rest of the questions assuming M has less than the maximum number of pivots. b. Are the rows of M linearly independent? No Yes O Need more information (could be either) c. Are the columns of M linearly independent? No Yes Need more information (could be either) d. How many solutions does Mv 0 have? Zero One = X Infinitely many Need more information (could be more than one of these) X e. How many solutions does Mv = b have for each b? Zero One Infinitely many Need more information (could be more than one of these)
Expert Solution
Step 1: Given

M is a 7 cross times 7 matrix

If a column is pivot in a matrix, its linearly independent column.

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