Solved find the rank of the following matrix

Question : Find row reduce form of the following matrix\[M=\left(\begin{matrix}3&-1&2&4\\9&-7&1&-2\end{matrix}\right)\]Solution :Given matrix\[M=\left(\begin{matrix}3&-1&2&4\\9&-7&1&-2\end{matrix}\right)\]To find rank of MStep 1:Applying elementary row transformation \(R_2\rightarrow R_2-3R_1\)\[M~\left(\begin{matrix}3&-1&2&4\\0&-4&-5&-14\\\end{matrix}\right)\]Step 2 :applying elementary row transformation \(R_1\rightarrow R_1-4R_2\)\[M~\left(\begin{matrix}3&0&22&60\\0&-4&-5&-14\end{matrix}\right)\]Step 3:Applying elementary row transformation \(R_1\rightarrow\frac{R_1}{3}\)\[M~\left(\begin{matrix}1&0&\frac{22}{3}&20\\0&-4&-5&-14\end{matrix}\right)\]Step 4:Applying elementary row transformation \(R_2\rightarrow\frac{R_2}{-4}\) \\[M~\left(\begin{matrix}1&0&\frac{22}{3}&20\\0&1&\frac{5}{4}&\frac{7}{2}\end{matrix}\right)\]Is…

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