Q61 / 160 · AP EAMCET 2004 · Mathematics

The rank of $\left[\begin{array}{ccc}1 & -1 & 1 \\ 1 & 1 & -1 \\ -1 & 1 & 1\end{array}\right]$ is

  • A
    $0$
  • B
    $1$
  • C
    $2$
  • Correct answer
    D
    $3$

Solution

$$ \begin{aligned} & \text { Let } A=\left[\begin{array}{ccc} 1 & -1 & 1 \\ 1 & 1 & -1 \\ -1 & 1 & 1 \end{array}\right] \\ & \therefore \quad|A|=1(1+1)+1(1-1)+1(1+1) \\ & =4 \neq 0 \\ & \end{aligned} $$ $\therefore$ Rank of matrix $A$ is 3 .

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

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