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Could a set of three vectors in R4 span all of R4? Explain. What about n vectors in Rm when n is less than m? Could a set of three vectors in R4 span all of R4? Explain. Choose the correct answer below. O A. No. The matrix A whose columns are the three vectors has four rows. To have a pivot in each row, A would have to have at least four columns (one for each pivot). B. Yes. Any number of vectors in R4 will span all of R4. C. No. There is no way for any number of vectors in R* to span all of R4. D. Yes. A set of n vectors in RM can span Rm when n< m. There is a sufficient number of rows in the matrix A formed by the vectors to have enough pivot points to show that the vectors span R™. Could a set of n vectors in RM span all of RM when n is less than m? Explain. Choose the correct answer below. O A. No. Without knowing values of n and m, there is no way to determine if n vectors in RM will span all of Rm. B. Yes. Any number of vectors in Rm will span all of Rm. c. No. The matrix A whose columns are the n vectors has m rows. To have a pivot in each row, A would have to have at least m columns (one for each pivot). O D. Yes. A set of n vectors in R™ can span R™ if n < m. There is a sufficient number of rows in the matrix A formed by the vectors to have enough pivot points to show that the vectors span Rm.

Could a set of three vectors in R4 span all of R4? Explain. What about n vectors in Rm when n is less than m? Could a set of three vectors in R4 span all of R4? Explain. Choose the correct answer below. O A. No. The matrix A whose columns are the three vectors has four rows. To have a pivot in each row, A would have to have at least four columns (one for each pivot). B. Yes. Any number of vectors in R4 will span all of R4. C. No. There is no way for any number of vectors in R* to span all of R4. D. Yes. A set of n vectors in RM can span Rm when n< m. There is a sufficient number of rows in the matrix A formed by the vectors to have enough pivot points to show that the vectors span R™. Could a set of n vectors in RM span all of RM when n is less than m? Explain. Choose the correct answer below. O A. No. Without knowing values of n and m, there is no way to determine if n vectors in RM will span all of Rm. B. Yes. Any number of vectors in Rm will span all of Rm. c. No. The matrix A whose columns are the n vectors has m rows. To have a pivot in each row, A would have to have at least m columns (one for each pivot). O D. Yes. A set of n vectors in R™ can span R™ if n < m. There is a sufficient number of rows in the matrix A formed by the vectors to have enough pivot points to show that the vectors span Rm.

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter2: Systems Of Linear Equations
Section2.2: Direct Methods For Solving Linear Systems
Problem 51EQ
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Could a set of three vectors in R4 span all of R4? Explain. What about n vectors in Rm when n is less than m? Could a set of three vectors in R4 span all of R4? Explain. Choose the correct answer below. A. No. The matrix A whose columns are the three vectors has four rows. To have a pivot in each row, A would have to have at least four columns (one for each pivot). B. Yes. Any number of vectors in R4 will span all of R4. O C. No. There is no way for any number of vectors in R4 to span all of R4. D. Yes. A set of n vectors in RM can span RM when n<m. There is a sufficient number of rows in the matrix A formed by the vectors to have enough pivot points to show that the vectors span Rm. Could a set of n vectors in Rm span all of RM when n is less than m? Explain. Choose the correct answer below. A. No. Without knowing values of n and m, there is no way to determine if n vectors in Rm will span all of Rm. B. Yes. Any number of vectors in Rm will span all of Rm. C. No. The matrix A whose columns are the n vectors has m rows. To have a pivot in each row, A would have to have at least m columns (one for each pivot). D. Yes. A set of n vectors in Rm can span R" if n<m. There is a sufficient number of rows in the matrix A formed by the vectors to have enough pivot points to show that the vectors span Rm.
Transcribed Image Text:Could a set of three vectors in R4 span all of R4? Explain. What about n vectors in Rm when n is less than m? Could a set of three vectors in R4 span all of R4? Explain. Choose the correct answer below. A. No. The matrix A whose columns are the three vectors has four rows. To have a pivot in each row, A would have to have at least four columns (one for each pivot). B. Yes. Any number of vectors in R4 will span all of R4. O C. No. There is no way for any number of vectors in R4 to span all of R4. D. Yes. A set of n vectors in RM can span RM when n<m. There is a sufficient number of rows in the matrix A formed by the vectors to have enough pivot points to show that the vectors span Rm. Could a set of n vectors in Rm span all of RM when n is less than m? Explain. Choose the correct answer below. A. No. Without knowing values of n and m, there is no way to determine if n vectors in Rm will span all of Rm. B. Yes. Any number of vectors in Rm will span all of Rm. C. No. The matrix A whose columns are the n vectors has m rows. To have a pivot in each row, A would have to have at least m columns (one for each pivot). D. Yes. A set of n vectors in Rm can span R" if n<m. There is a sufficient number of rows in the matrix A formed by the vectors to have enough pivot points to show that the vectors span Rm.
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