Question

A system of linear simultaneous equations is given as AX = b, where A = $\left[\begin{array}{cccc}1& 0& 1& 0\\ 0& 1& 0& 1\\ 1& 1& 0& 0\\ 0& 0& 0& 1\end{array}\right]$ and b = $\left[\begin{array}{c}0\\ 0\\ 0\\ 1\end{array}\right]$, then the rank of matrix A is

• A. 1
• B. 2
• C. 3
• D. 4

Answer 1

The correct option is D 4

Given A = $\left[\begin{array}{cccc}1& 0& 1& 0\\ 0& 1& 0& 1\\ 1& 1& 0& 0\\ 0& 0& 0& 1\end{array}\right]$

$R_3\to R_3-R_1$
A $\sim \left[\begin{array}{cccc}1& 0& 1& 0\\ 0& 1& 0& 1\\ 0& 1& -1& 0\\ 0& 0& 0& 1\end{array}\right]$

$R_3\to R_3-R_2$

A $\sim \left[\begin{array}{cccc}1& 0& 1& 0\\ 0& 1& 0& 1\\ 0& 1& -1& 0\\ 0& 0& 0& 1\end{array}\right]$ (Echelon Form)

So, p(A) = 4