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