Question

The rank of the matrix $A=\left[\begin{array}{cccc}2& 3& 1& 4\\ 0& 1& 2& -1\\ 0& -2& -4& 2\end{array}\right]$ is

• A. 2
• B. 3
• C. 1
• D. indeterminate

Answer 1

The correct option is A 2

Given $A=\left[\begin{array}{cccc}2& 3& 1& 4\\ 0& 1& 2& -1\\ 0& -2& -4& 2\end{array}\right]$
Rank of A $\le min$ $3,4$
So, rank of $A\le 3$
Now, we will reduce it to Echelon form
$R_3\to R_3+2R_2$
$\left[\begin{array}{cccc}2& 3& 1& 4\\ 0& 1& 2& -1\\ 0& 0& 0& 0\end{array}\right]$
Here, row $R_3$ has all elements 0.
So, two non-zero rows.
Hence, rank =2