Suppose a matrix A has n rows and m columns. Select the best statement. (The best condition should work with any positive integer n.) O A. If n < m then the m columns of A span R" as long as the columns are distinct. O B. If n < m then the m columns of A span R" as long as no column is a scalar multiple of another column. OC. If n < m then the m columns of A span R“ as long as no column is is the zero vector. O D. If n < m then the m columns of A may span R“. O E. If n < m then the m columns of A cannot span R". OF. If n < m then the m columns of A must span R". O G. none of the above

Algebra and Trigonometry (6th Edition)
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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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A12: Problem 5
Previous Problem
Problem List
Next Problem
Suppose a matrix A hasn rows and m columns.
Select the best statement. (The best condition should work with any positive integer n.)
O A. If n < m then the m columns of A span R" as long as the columns are distinct
B. If n < m then the m columns of A span R' as long as no column is a scalar multiple of another column.
C. If n < m then the m columns of A span R" as long as no column is is the zero vector.
OD. If n < m then the m columns of A may span R".
E. If n < m then the m columns of A cannot span R".
OF. If n < m then the m columns of A must span R".
G. none of the above
Transcribed Image Text:A12: Problem 5 Previous Problem Problem List Next Problem Suppose a matrix A hasn rows and m columns. Select the best statement. (The best condition should work with any positive integer n.) O A. If n < m then the m columns of A span R" as long as the columns are distinct B. If n < m then the m columns of A span R' as long as no column is a scalar multiple of another column. C. If n < m then the m columns of A span R" as long as no column is is the zero vector. OD. If n < m then the m columns of A may span R". E. If n < m then the m columns of A cannot span R". OF. If n < m then the m columns of A must span R". G. none of the above
Assume {u1, u2, U3 , U4 } does not
R³.
span
Select the best statement.
A. {u1, u2, u3 } spans R if u4 is a scalar multiple of another vector in the set.
B. {u1, u2, ul3 } spans R if u4 is the zero vector.
C. {u1, u2, u3 } spans R' if u4 is a linear combination of other vectors in the set.
D. There is no easy way to tell if {u1, u2, u3 } spans R'.
E. {u1 , u2, u3 } cannot span R’.
F. none of the above
Transcribed Image Text:Assume {u1, u2, U3 , U4 } does not R³. span Select the best statement. A. {u1, u2, u3 } spans R if u4 is a scalar multiple of another vector in the set. B. {u1, u2, ul3 } spans R if u4 is the zero vector. C. {u1, u2, u3 } spans R' if u4 is a linear combination of other vectors in the set. D. There is no easy way to tell if {u1, u2, u3 } spans R'. E. {u1 , u2, u3 } cannot span R’. F. none of the above
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