Determine whether the statement below is true or false. Justify the answer. The pivot positions in a matrix depend on whether row interchanges are used in the row reduction process. O A. The statement is false. The pivot positions in a matrix depend on the location of the pivot column. O B. The statement is false. The pivot positions in a matrix are determined completely by the positions of the leading entries in the nonzero rows of any echelon form obtained from the matrix. O C. The statement is true. Every pivot position is determined by the positions of the leading entries of a matrix in reduced echelon form. O D. The statement is true. The pivot positions in a matrix are determined completely by the positions of the leading entries of each row which are dependent on row interchanges.
Determine whether the statement below is true or false. Justify the answer. The pivot positions in a matrix depend on whether row interchanges are used in the row reduction process. O A. The statement is false. The pivot positions in a matrix depend on the location of the pivot column. O B. The statement is false. The pivot positions in a matrix are determined completely by the positions of the leading entries in the nonzero rows of any echelon form obtained from the matrix. O C. The statement is true. Every pivot position is determined by the positions of the leading entries of a matrix in reduced echelon form. O D. The statement is true. The pivot positions in a matrix are determined completely by the positions of the leading entries of each row which are dependent on row interchanges.
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:Determine whether the statement below is true or false. Justify the answer.
The pivot positions in a matrix depend on whether row interchanges are used in the row reduction process.
O A. The statement is false. The pivot positions in a matrix depend on the location of the pivot column.
O B. The statement is false. The pivot positions in a matrix are determined completely by the positions of the leading entries in the
nonzero rows of any echelon form obtained from the matrix.
O C. The statement is true. Every pivot position is determined by the positions of the leading entries of a matrix in reduced echelon form.
O D. The statement is true. The pivot positions in a matrix are determined completely by the positions of the leading entries of each row
which are dependent on row interchanges.
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