Q44 / 160 · AP EAMCET 2023 (17 May Shift 2) · Mathematics

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

  • A
    3
  • Correct answer
    B
    2
  • C
    4
  • D
    1

Solution

The given matrix is $A=\left[\begin{array}{cccc}1 & 1 & 1 & 3 \\ 2 & 2 & -1 & 3 \\ 1 & 1 & -1 & 1\end{array}\right]$ $\mathrm{R}_2 \rightarrow 2 \mathrm{R}_1-\mathrm{R}_2, \mathrm{R}_3 \rightarrow \mathrm{R}_1-\mathrm{R}_3$ $A=\left[\begin{array}{llll}1 & 1 & 1 & 3 \\ 0 & 0 & 3 & 3 \\ 0 & 0 & 2 & 2\end{array}\right]$ $\mathrm{R}_2 \rightarrow \frac{\mathrm{R}_2}{3}, R_3 \rightarrow \frac{\mathrm{R}_3}{2}$ $\approx\left[\begin{array}{llll}1 & 1 & 1 & 3 \\ 0 & 0 & 1 & 1 \\ 0 & 0 & 1 & 1\end{array}\right]$ Rank $(A)=$ No of non-zero rows $=2$ $\approx\left[\begin{array}{llll}1 & 1 & 1 & 3 \\ 0 & 0 & 1 & 1 \\ 0 & 0 & 0 & 0\end{array}\right]$

Hence, the correct answer is option: 'B'.

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