What is the rank of the matrix $\left[\begin{array}{lll}1 & 1 & 1 \\ 1 & 1 & 1 \\ 1 & 1 &…

What is the rank of the matrix $\left[\begin{array}{lll}1 & 1 & 1 \\ 1 & 1 & 1 \\ 1 & 1 & 1\end{array}\right]=$ ?
  1. 2
  2. 1
  3. 3
  4. 0

Solution

$A=\left[\begin{array}{lll}1 & 1 & 1 \\ 1 & 1 & 1 \\ 1 & 1 & 1\end{array}\right]$, Convert it into row echelon form by applying row transformation as follows $ \begin{aligned} & R_2 \rightarrow R_2-R_1, R_3 \rightarrow R_3-R_1 \\ & A \sim\left[\begin{array}{lll} 1 & 1 & 1 \\ 0 & 0 & 0 \\ 0 & 0 & 0 \end{array}\right] \end{aligned} $ Number of non-zero row in echelon form of matrix is 1 . $\therefore$ Rank of $A=1$

Asked in: AP EAMCET 2021 (23 Aug Shift 1)

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