Examples are the best way to understand a complicated view. Let’s directly dive into the example of this topic.

Let us consider a matrix. name the matrix as A.

Now let us break this into 2 two-stage processes.

1. Echelon form:
2. Count the non-zero rows.

STEP 1: LET US TAKE ECHELON FORM:

• Subtract 2 times the first row from the second row:

• Subtract the first row from the third row:

Let’s take now the values which have been generated so far

• Now multiply the third row by -1 

By the result of this we get a positive leading factor.

STEP 2: let’s COUNT THE NON-ZERO ROWS:

Before this lets us conclude the definition of the rank of a matrix

RANK OF MATRIX = NO. OF. ZERO ROW  IN ECHELON FORM HENCE WE CAN CONCLUDE THAT THE RANK OF THE MATRIX IS 2