Question

The rank of an nxn matrix each of words
whose elements is
2 is​

Answer 1

So a general way of finding the rank of the matrix is by reducing it to it's Row Echelon Form (note that row-reduced echelon form is not necessary). You just have to make all the elements zero below the pivot elements. So you have:

⎡⎣⎢147258369⎤⎦⎥−→−−−−−−R3=R3−7R1R2=R2−4R1⎡⎣⎢100 2−3−6 3−6−12⎤⎦⎥−→−−−−−−R3=R3−2R2⎡⎣⎢100 2−3 0 3−6 0⎤⎦⎥

After reducing it you just have to count the number of non-zero rows and that's your rank. Here as you can see it's 2. This can help you find the rank of any matrix.