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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. No. There is no way for any number of vectors in R4 to span all of R4. C. Yes. A set of n vectors in Rm can span Rm when n

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. No. There is no way for any number of vectors in R4 to span all of R4. C. Yes. A set of n vectors in Rm can span Rm when n

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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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. No. There is no way for any number of vectors in R4 to span all of R4. OC. 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. D. Yes. Any number of vectors in R4 will span all of R4.
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. 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. No. There is no way for any number of vectors in R4 to span all of R4. OC. 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. D. Yes. Any number of vectors in R4 will span all of R4.
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