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Is the row rank always equal to the column rank, e.g. is the rank of the matrix = row rank = column rank? | Is the row rank always equal to the column rank, e.g. is the rank of the matrix = row rank = column rank? | ||
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| + | Answer from [[User:Bell|Steve Bell]]: | ||
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| + | Yes, it is a fact that the dimension of the row space is equal to the dimension of the column space. See Theorem 6 on p. 286. | ||
[[2013 Fall MA 527 Bell|Back to MA527, Fall 2013]] | [[2013 Fall MA 527 Bell|Back to MA527, Fall 2013]] | ||
[[Category:MA527Fall2013Bell]] [[Category:MA527]] [[Category:Math]] | [[Category:MA527Fall2013Bell]] [[Category:MA527]] [[Category:Math]] | ||
Revision as of 08:41, 26 September 2013
Practice problems for Exam 1 discussion area
Discuss the old exam and the practice problems here. (You can find them on the MA 527 home page.)
Question from Katherine Mathews
I have a general question... When finding a real solution from a complex solution, do you only need to use one of the eigen-vectors? Each example that was done in class, you only completed the real solution from one eigen-vector and I am not sure if that was done for time sake or if that is the complete solution. If the complete solution can be determined from one eigen-vector complex eigen-vector, does it matter which one you pick?
Question:
When solving a non-homogeneous solution, if we prefer using method of variation of parameters instead of method of undetermined coefficients, is it necessary to know how to use the latter in a question, or is it sufficient to know/understand one of the two methods (either one)?
Question from Kees
Is the row rank always equal to the column rank, e.g. is the rank of the matrix = row rank = column rank?
Answer from Steve Bell:
Yes, it is a fact that the dimension of the row space is equal to the dimension of the column space. See Theorem 6 on p. 286.
