If the ranks of the matrices $A=\left[\begin{array}{ccc}1 & 0 & 1 \ 2 & 1 & 2 \ 1 & 0 & -1\end{array} ight]$ and $B=\left[\begin{array}{cccc}1 & 2 & 3 & 4 \ 2 & 4 & 6 & -8\end{array} ight]$ are $r_1$ and $r_2$ respectively then $r_1-r_2=$

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If the ranks of the matrices $A=\left[\begin{array}{ccc}1 & 0 & 1 \ 2 & 1 & 2 \ 1 & 0 & -1\end{array}ight]$ and $B=\left[\begin{array}{cccc}1 & 2 & 3 & 4 \ 2 & 4 & 6 & -8\end{array}ight]$ are $r_1$ and $r_2$ respectively then $r_1-r_2=$

Aicharya · Accepted Answer

$A=\left[\begin{array}{ccc}1 & 0 & 1 \ 2 & 1 & 2 \ 1 & 0 & -1\end{array}ight]$ $ |\mathrm{A}|=1(-1-0)+1(0-1)=-1-1=-2=0 $ $	herefore$ Rank of $\mathrm{A}\left(\mathrm{r}_1ight)=3$ $ \begin{aligned} & \mathrm{B}=\left[\begin{array}{cccc} 1 & 2 & 3 & 4 \ 2 & 4 & 6 & -8 \end{array}ight] \ & \because\left|\begin{array}{cc} 3 & 4 \ 6 & -8 \end{array}ight|=-24-24=-48 
eq 0 \end{aligned} $ $	herefore$ Rank of $B\left(r_2ight)=2$ Now, $\mathrm{r}_1-\mathrm{r}_2=3-2=1$

If the ranks of the matrices $A=\left[\begin{array}{ccc}1 & 0 & 1 \\ 2 & 1 & 2 \\ 1 & 0 &…

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