How to determine the rank of a matrix?

first the definition of the rank of a matrix is "maximal number of linearly independent column vectors in the matrix"

then the question could be rephrased to " how many independent column vectors are there".

so what we want to do is actually to find how many independent column vectors this matrix has.

to find the number of independent columns, use Elementary Row Operations (would be demonstrated with an example matrix in detail in real class) to find the rank.

Something further things to note after covering the main thing above:

1. The above method can be used to find the rank of a matrix, be it square or not.

2. To save the calculation, determininant of a square matrix can be checked beforehand,  if it is non zero then the rank is its number of columns (rows).

3. If the matrix is a zero matrix, its rank is 0.