Suppose A is a 5x7 matrix. How many pivot columns must A have if its columns span Rº? Why? Select the correct choice below and, if necessary, fill in the answer box to complete your choice. O A. The matrix must have pivot columns. The statements "A has a pivot position in every row" and "the columns of A span R5" are logically equivalent. OB. The matrix must have pivot columns. Otherwise, the equation Ax=0 would have a free variable, in which case the columns of A would not span RS. OC. The matrix must have pivot columns. If A had fewer pivot columns, then the equation Ax=0 would have only the trivial solution. OD. The columns of a 5x7 matrix cannot span R³ because having more columns than rows makes the columns of the matrix dependent.
Suppose A is a 5x7 matrix. How many pivot columns must A have if its columns span Rº? Why? Select the correct choice below and, if necessary, fill in the answer box to complete your choice. O A. The matrix must have pivot columns. The statements "A has a pivot position in every row" and "the columns of A span R5" are logically equivalent. OB. The matrix must have pivot columns. Otherwise, the equation Ax=0 would have a free variable, in which case the columns of A would not span RS. OC. The matrix must have pivot columns. If A had fewer pivot columns, then the equation Ax=0 would have only the trivial solution. OD. The columns of a 5x7 matrix cannot span R³ because having more columns than rows makes the columns of the matrix dependent.
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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Transcribed Image Text:Suppose A is a 5x7 matrix. How many pivot columns must A have if its columns span R5? Why?
Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
pivot columns. The statements "A has a pivot position in every row" and "the columns of A span R³" are logically equivalent.
5
O A. The matrix must have
OB. The matrix must have pivot columns. Otherwise, the equation Ax=0 would have a free variable, in which case the columns of A would not span R
OC. The matrix must have pivot columns. If A had fewer pivot columns, then the equation Ax=0 would have only the trivial solution.
D. The columns of a 5x7 matrix cannot span R5 because having more columns than rows makes the columns of the matrix dependent.
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