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
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
100%
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
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 2 steps with 1 images
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
