# How to calculate the rank of a matrix

Last updated: Jan. 2, 2019
Calculate the rank of the following matrices.
$(a)$
$(b)$

$(a)$
Let $A$ be an matrix defined as
. We transform $A$ to the reduced row echelon form as follows.
As a result of this transformation, since the matrix has two leading entries, we see that the rank of $A$ is $2$.
$(b)$
Let $B$ be an matrix defined as
. We transform $B$ to the reduced row echelon form as follows.
As a result of this transformation, since the matrix has three leading entries, we see that the rank of $B$ is $3$.