Suppose A is a 7x5 matrix. How many pivot columns must A have if its columns are linearly independent? Why? Select the correct answer below. pivot columns. If A had fewer pivot columns, then the equation Ax = 0 would have only the trivial solution. OA. The matrix must have OB. The matrix must have pivot columns. The statements "A has a pivot position in every row" and "the columns of A are linearly independent" are logically equivalent. OC. The matrix must have pivot columns. Otherwise, the equation Ax=0 would have a free variable, in which case the columns of A would be linearly dependent. O D. None of the columns of A are pivot columns. Any column of A that is a pivot column is linearly dependent with the other pivot columns.
Suppose A is a 7x5 matrix. How many pivot columns must A have if its columns are linearly independent? Why? Select the correct answer below. pivot columns. If A had fewer pivot columns, then the equation Ax = 0 would have only the trivial solution. OA. The matrix must have OB. The matrix must have pivot columns. The statements "A has a pivot position in every row" and "the columns of A are linearly independent" are logically equivalent. OC. The matrix must have pivot columns. Otherwise, the equation Ax=0 would have a free variable, in which case the columns of A would be linearly dependent. O D. None of the columns of A are pivot columns. Any column of A that is a pivot column is linearly dependent with the other pivot columns.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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Transcribed Image Text:Suppose A is a 7x5 matrix. How many pivot columns must A have if its columns are linearly independent? Why?
Select the correct answer below.
C
pivot columns. If A had fewer pivot columns, then the equation Ax=0 would have only the trivial solution.
OA. The matrix must have
O B. The matrix must have pivot columns. The statements "A has a pivot position in every row" and "the columns of A are linearly independent" are logically equivalent.
O C. The matrix must have pivot columns. Otherwise, the equation Ax = 0 would have a free variable, in which case the columns of A would be linearly dependent.
O D. None of the columns of A are pivot columns. Any column of A that is a pivot column is linearly dependent with the other pivot columns.
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