Understanding the Rank of a Matrix: Explained Simply

[Taryn]

Hey I am just wondering about this question... I have reduced it as much as I can and the second part of the question is asking about the rank of the matrix... which means the leading number of ones right?

SO if I had this matrix 2 5 0
0 2 1
0 0 0

Wat would be the leading ones and would the last row be classed as leading ones? If you can just giv a brief explanation that would be great! I understand wat I meant to be finding just am a lil unsure of the concept!

Would the rank be 2?

 

[Taryn]

the matrix was meant to be

2 5 0
0 2 1
0 0 0

sorry if it doesn't look right in the above post!

 

[courtrigrad]

If $$A = \begin{bmatrix} 2 & 5 & 0 \\ 0 & 2 & 1 \\ 0 & 0 & 0 \\ \end{bmatrix}$$

then the rank is 2. The rank is just the number of non-zero rows.

 

[Taryn]

ahhh that's easy! Thanks... also just wonderin if you had 2 rows that were identical then the rank would just be 1 right?

 

[courtrigrad]

yes, because they are not linearly independent