realtion between columns and rows of a matrix and space

HelpNeeder

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Feb 17, 2021
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Suppose A is an mxn matrix.
The columns of A span Rm. Why is it Rm and not Rn?
 

lex

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Mar 3, 2021
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When you multiply a column vector containing n elements, by a matrix with m rows (and n columns) you get a column vector with m rows.
Remember when you multiply Ax you are getting a linear combination of the columns of matrix A (each of which contains m elements).
1617818442764.png
 

HelpNeeder

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Feb 17, 2021
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Thank you. I understand it now.
 

Jomo

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Dec 30, 2014
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No one can answer your question since you never gave the size of matrix A. Do you see that? Having said that, Lex gave a good response.
 
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