Question

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

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

Answer 1

The correct option is A

2

Given $\begin{array}{c}A=\left[\begin{array}{cccc}2& 3& 1& 4\\ 0& 1& 2& -1\\ 0& -2& -4& 2\end{array}\right],(R_2\to 2R_2+R_3)\end{array}$

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

Since every minor of order 3 in A is 0 and there exists a minor order 3 i.e. $\begin{array}{c}\left[\begin{array}{cc}2& 3\\ 0& -2\end{array}\right]\end{array}$ in A which is non-zero.

Thus, rank = 2.