iii) If \( A=\left[\begin{array}{cc}3 & 4 \\ -2 & 5\end{array}\right] \) then apply \( R_{1}+3 R_{2} \) elementary transformation.
iii) If \( A=\left[\begin{array}{cc}3 & 4 \\ -2 & 5\end{array}\right] \) then apply \( R_{1}+3 R_{2} \) elementary transformation.
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\(A=\begin{bmatrix}3&4\\-2&5\end{bmatrix}\)
Applying R1 → R1 + 3R2
Then \(A\sim\begin{bmatrix}3+3\times-2&4+3\times5\\-2&5\end{bmatrix}\)
\(=\begin{bmatrix}3-6&4+15\\-2&5\end{bmatrix}\)
\(=\begin{bmatrix}-3&19\\-2&5\end{bmatrix}\)
After applying transformation R1 → R1 + 3R2 the elementary matrix of A is \(\begin{bmatrix}-3&19\\-2&5\end{bmatrix}.\)
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