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Question: Adding rows to matrix

Question:Adding rows to matrix

schzan 130
matrix linearalgebra vector
January 10 2016
1

Suppose we are given a matrix M[n*2n] of n linearly independent row vectors. Then I am trying to create a procedure to add n more linearly independent row vectors to this matix resulting in to a matrix M[2n*2n].

Consider this easy example, if the given matrix $M_{2*4}$ is

Matrix(2, 4, {(1, 1) = 4, (1, 2) = 1, (1, 3) = 0, (1, 4) = 0, (2, 1) = 0, (2, 2) = 0, (2, 3) = 4, (2, 4) = 1}) 
then we can add $[0,0,0,1]$ and $[0,0,1,0]$ to obtain the matrix $M_{4*4}$

Matrix(4, 4, {(1, 1) = 4, (1, 2) = 1, (1, 3) = 0, (1, 4) = 0, (2, 1) = 0, (2, 2) = 0, (2, 3) = 4, (2, 4) = 1, (3, 1) = 1, (3, 2) = 0, (3, 3) = 0, (3, 4) = 0, (4, 1) = 0, (4, 2) = 0, (4, 3) = 1, (4, 4) = 0})

 

Can I use rref form?Thank you for your help.

 
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