Question

Given matrix $\left[A\right]=\left[\begin{array}{cccc}4& 2& 1& 3\\ 6& 3& 4& 7\\ 2& 1& 0& 1\end{array}\right]$. The rank of the matrix is _____ .

• A. 4
• B. 3
• C. 2
• D. 1

Answer 1

The correct option is C 2

$\left[A\right]=\left[\begin{array}{cccc}4& 2& 1& 3\\ 6& 3& 4& 7\\ 2& 1& 0& 1\end{array}\right]$

$R_1\to R_1-2R_3$

$R_2\to R_2-3R_3$

$\sim \left[\begin{array}{cccc}0& 0& 1& 1\\ 0& 0& 4& 4\\ 2& 1& 0& 1\end{array}\right]$

$R_2\to R_2-4R_1$

$\sim \left[\begin{array}{cccc}0& 0& 1& 1\\ 0& 0& 0& 0\\ 2& 1& 0& 1\end{array}\right]$
Number of non-zero rows=2

$\Rightarrow Rank\left(A\right)=2$