rank of matrix 3 by3 order by solution

Question

rank of ⌈0 2 3]

           ι0 4 6ι

           ⌊0 6 9⌋       

Answer 1

Hi Sikandar. If I am reading this matrix correctly, it seems the rows 2 and 3 are just factors row of 1. That is, we can obtain row 2 by multiplying row 1 by 2, and we can obtain row 3 by multiplying row 1 by 3. So Naturally, we can reduce the matrix to   0 2 3 
                      0 0 0
                      0 0 0 

Thus the rank is only 1! Hope this helps.
   

Answer 2

The second row is twice the first row and the third row is three times the first row, so the matrix can be row reduced to the matrix that has first row [0 2 3] and zeros elsewhere. Hence, the rank is 1.