The rank of the following matrix $A$ is $$ A=\left[\begin{array}{cccc} 1 & -2 & 3 & -4 \\ 2 & 9 & 4 & 5 \\ 4…

The rank of the following matrix $A$ is $$ A=\left[\begin{array}{cccc} 1 & -2 & 3 & -4 \\ 2 & 9 & 4 & 5 \\ 4 & 5 & 10 & -3 \\ 1 & 11 & -1 & 9 \end{array}\right\rfloor $$
  1. 4
  2. 3
  3. 2
  4. 1

Solution

Given matrix $A=\left[\begin{array}{cccc}1 & -2 & 3 & -4 \\ 2 & 9 & 4 & 5 \\ 4 & 5 & 10 & -3 \\ 1 & 11 & -1 & 9\end{array}\right]$ $R_3 \rightarrow R_3-\left(R_2+2 R_1\right)$ and $R_4 \rightarrow R_4-\left(R_2-R_1\right)$ or $A=\left[\begin{array}{cccc}1 & -2 & 3 & -4 \\ 2 & 9 & 4 & 5 \\ 0 & 0 & 0 & 0 \\ 0 & 0 & -2 & 0\end{array}\right]$ So rank $(A)=3$.

Asked in: AP EAMCET 2018 (23 Apr Shift 2)

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