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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. 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 be linearly dependent. O C. 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 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. 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 be linearly dependent. O C. 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 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
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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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. 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 be linearly dependent. O C. 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 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.
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. pivot columns. If A had fewer pivot columns, then the equation Ax=0 would have only the trivial solution. 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 be linearly dependent. O C. 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 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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If A is m×n matrix with m>n then number of pivot columns is equal to number of linearly independent columns 

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