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If A is a 10x7 matrix, what is the largest possible rank of A? If A is a 7x 10 matrix, what is the largest possible rank of A? Explain your answers. Select the correct choice below and fill in the answer box(es) to complete your choice. O A. The rank of A is equal to the number of pivot positions in A. Since there are only 7 columns in a 10x7 matrix, and there are only 7 rows in a 7x 10 matrix, there can be at most pivot positions for either matrix. Therefore, the largest possible rank of either matrix is O B. The rank of A is equal to the number of columns of A. Since there are 7 columns in a 10x7 matrix, the largest possible rank of a 10x7 matrix is Since there are 10 columns in a 7x 10 matrix, the largest possible rank of a 7x 10 matrix is O C. The rank of A is equal to the number of non-pivot columns in A. Since there are more rows than columns in a 10x7 matrix, the rank of a 10x7 matrix must be equal to . Since there are 7 rows in a 7x 10 matrix, there are a maximum of 7 pivot positions in A. Thus, there are 3 non-pivot columns. Therefore, the largest possible rank of a 7x 10 matrix is

If A is a 10x7 matrix, what is the largest possible rank of A? If A is a 7x 10 matrix, what is the largest possible rank of A? Explain your answers. Select the correct choice below and fill in the answer box(es) to complete your choice. O A. The rank of A is equal to the number of pivot positions in A. Since there are only 7 columns in a 10x7 matrix, and there are only 7 rows in a 7x 10 matrix, there can be at most pivot positions for either matrix. Therefore, the largest possible rank of either matrix is O B. The rank of A is equal to the number of columns of A. Since there are 7 columns in a 10x7 matrix, the largest possible rank of a 10x7 matrix is Since there are 10 columns in a 7x 10 matrix, the largest possible rank of a 7x 10 matrix is O C. The rank of A is equal to the number of non-pivot columns in A. Since there are more rows than columns in a 10x7 matrix, the rank of a 10x7 matrix must be equal to . Since there are 7 rows in a 7x 10 matrix, there are a maximum of 7 pivot positions in A. Thus, there are 3 non-pivot columns. Therefore, the largest possible rank of a 7x 10 matrix is

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter3: Matrices
Section3.1: Matrix Operations
Problem 19EQ: A factory manufactures three products (doohickies, gizmos, and widgets) and ships them to two...
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If A is a 10x7 matrix, what is the largest possible rank of A? If A is a 7x 10 matrix, what is the largest possible rank of A? Explain your answers. .... Select the correct choice below and fill in the answer box(es) to complete your choice. O A. The rank of A is equal to the number of pivot positions in A. Since there are only 7 columns in a 10x7 matrix, and there are only 7 rows in a 7x 10 matrix, there can be at most pivot positions for either matrix. Therefore, the largest possible rank of either matrix is O B. The rank of A is equal to the number of columns of A. Since there are 7 columns in a 10 x7 matrix, the largest possible rank of a 10 x7 matrix is Since there are 10 columns in a 7x10 matrix, the largest possible rank of a 7x 10 matrix is O C. The rank of A is equal to the number of non-pivot columns in A. Since there are more rows than columns in a 10x7 matrix, the rank of a 10 x7 matrix must be equal to Since there are 7 rows in a 7x 10 matrix, there are a maximum of 7 pivot positions in A. Thus, there are 3 non-pivot columns. Therefore, the largest possible rank of a 7x 10 matrix is
Transcribed Image Text:If A is a 10x7 matrix, what is the largest possible rank of A? If A is a 7x 10 matrix, what is the largest possible rank of A? Explain your answers. .... Select the correct choice below and fill in the answer box(es) to complete your choice. O A. The rank of A is equal to the number of pivot positions in A. Since there are only 7 columns in a 10x7 matrix, and there are only 7 rows in a 7x 10 matrix, there can be at most pivot positions for either matrix. Therefore, the largest possible rank of either matrix is O B. The rank of A is equal to the number of columns of A. Since there are 7 columns in a 10 x7 matrix, the largest possible rank of a 10 x7 matrix is Since there are 10 columns in a 7x10 matrix, the largest possible rank of a 7x 10 matrix is O C. The rank of A is equal to the number of non-pivot columns in A. Since there are more rows than columns in a 10x7 matrix, the rank of a 10 x7 matrix must be equal to Since there are 7 rows in a 7x 10 matrix, there are a maximum of 7 pivot positions in A. Thus, there are 3 non-pivot columns. Therefore, the largest possible rank of a 7x 10 matrix is
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