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May 9th, 2015, 11:12 AM  #1 
Newbie Joined: Oct 2013 Posts: 29 Thanks: 1  Relationship between the rows of three matrices
Hello, I'm having trouble with the following problem: We solve a system of homogenous linear equations given by the matrix A and we write the basis of its solution space into the rows of the matrix B. Next, we solve the system Bx=0 and we write the basis of its solution space into the rows of matrix C. What is the relationship in between the rows of matrices A, B and C? 1) The rows of C are linear combinations of the rows of A, but it is possible that a row of A exists such that it is not a linear combination of the rows of C. 2)The rows of B are linear combinations of the rows of A or the rows of C. 3)The linear span of the rows of A is equivalent to that of rows of C. 4)The number of rows of C is greater than the number of rows of A. 5) Nothing above is generally true. I hold a strong suspicion that the answer is 5). The reasoning behind this is the fact that the matrix A might be regular, and therefore the dimension of its solution space is 0 => we don't write anything into B nor C and that invalidates every answer apart from 5). However, I am not entirely sure, so I would like to get a confirmation or refutation. Any input would be greatly welcome, thanks! 

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matrices, relationship, rows 
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