Question

The rank of the matrix \[ A= \begin{pmatrix} 1&2&3\\ 2&1&0\\ 0&1&2 \end{pmatrix} \]is

• A. 0
• B. 1
• C. 3
• D. 2

Hint:

For a \(3\times3\) matrix: \[ \boxed{ \begin{aligned} \det(A)\neq0 &\Rightarrow \text{Rank}=3 \det(A)=0 &\Rightarrow \text{Check row reduction} \end{aligned} } \] Here, \[ R_2=-3R_3, \] so only two independent rows exist.

Answer 1

The Correct Option is D