(B) Let $A = \left[\begin{array}{lll}1 & 1 & 1 \\ 1 & 1 & 1 \\ 1 & 1 & 1\end{array}\right]$.To find the rank,we convert the matrix into row echelon fo

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(B) Let $A = \left[\begin{array}{lll}1 & 1 & 1 \\ 1 & 1 & 1 \\ 1 & 1 & 1\end{array}\right]$.To find the rank,we convert the matrix into row echelon form using row transformations:Apply $R_2 \rightarrow R_2 - R_1$ and $R_3 \rightarrow R_3 - R_1$:$A \sim \left[\begin{array}{lll}1 & 1 & 1 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{array}\right]$.The number of non-zero rows in the row echelon form of the matrix is $1$.Therefore,the rank of $A$ is $1$.

Class 12 Mathematics 3 and 4 .Determinants and Matrices Rank of Matrices , Some special determinants, differentiation and integration of determinants

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What is the rank of the matrix $\left[\begin{array}{lll}1 & 1 & 1 \\ 1 & 1 & 1 \\ 1 & 1 & 1\end{array}\right]$?

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A
$2$
B
$1$
C
$3$
D
$0$

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3 and 4 .Determinants and Matrices

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Rank of Matrices , Some special determinants, differentiation and integration of determinants

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