Question

The rank of matrix A = $\left[\begin{array}{ccc}1& 2& 3\\ 3& 4& 5\\ 4& 6& 8\end{array}\right]$ is

• A. 0
• B. 1
• C. 2
• D. 3

Answer 1

The correct option is C 2

Given A= $\left[\begin{array}{ccc}1& 2& 3\\ 3& 4& 5\\ 4& 6& 8\end{array}\right]$

$R_2\to R_2-3R_1;R_3\to R_3-4R_1$

$A\sim \left[\begin{array}{ccc}1& 2& 3\\ 0& -2& -4\\ 0& -2& -4\end{array}\right]$

$R_3\to R_3-R_2$

$A\sim \left[\begin{array}{ccc}1& 2& 3\\ 0& -2& -4\\ 0& 0& 0\end{array}\right]$
Number of non-zero rows = 2

So $\rho \left(A\right)=2$