Let $A=\left[\begin{array}{cccc}1 & 0 & -1 & -3 \ 0 & 1 & 1 & k-1 \ 0 & 0 & k-1 & 1\end{array} ight]$ and $k \in R$. Then, the value of $k$, if exists, for which the rank of $A$ is 2 , is

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Let $A=\left[\begin{array}{cccc}1 & 0 & -1 & -3 \ 0 & 1 & 1 & k-1 \ 0 & 0 & k-1 & 1\end{array}ight]$ and $k \in R$. Then, the value of $k$, if exists, for which the rank of $A$ is 2 , is

Aicharya · Accepted Answer

Given, $A=\left[\begin{array}{cccc}1 & 0 & -1 & -3 \ 0 & 1 & 1 & k-1 \ 0 & 0 & k-1 & 1\end{array}ight]$ Applying $R_2 ightarrow R_2+R_3$, $ A=\left[\begin{array}{cccc} 1 & 0 & -1 & -3 \ 0 & 1 & k & k \ 0 & 0 & k-1 & 1 \end{array}ight] $ The value of $k$ does not exists as the rank of 2 is not possible in this case

Let $A=\left[\begin{array}{cccc}1 & 0 & -1 & -3 \\ 0 & 1 & 1 & k-1 \\ 0 & 0 & k-1 & 1\end{array}\right]$ and…

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