Elementary Operation (Transformation) of a Matrix

If $A=\left[\begin{array}{cc}2& 1\\ 1& 2\end{array}\right]$. Find new matrix obtained after transformation $R_1+2R_2$.

If $A=\left[\begin{array}{cc}5& 2\\ 1& 6\end{array}\right]$ and $C_i, R_i$ represents $i^{th}$ column and row respectively, find new matrix obtained for $2R_1, 3R_2$.

If $A=\left[\begin{array}{cc}4& 5\\ 1& 2\end{array}\right]$ and $C_i, R_i$ represents $i^{th}$ column and row respectively, find new matrix obtained for $2R_1, 3R_2$.

Transform $\left[\begin{array}{ccc}1& -1& 2\\ 2& 1& 3\\ 3& 2& 4\end{array}\right]$ into an upper triangular matrix by using the suitable row transformations.

Show that matrices $A$ and $B$ are row equivalent if $A=\left[\begin{array}{ccc}1& -1& 0\\ 2& 1& 1\end{array}\right]$ and $B=\left[\begin{array}{lll}3& 0& 1\\ 0& 3& 1\end{array}\right]$.

Transform $\left[\begin{array}{ccc}1& 2& 3\\ 2& 5& 7\\ 3& 1& 2\end{array}\right]$ into an upper triangular matrix by using the suitable row transformations.

Transform $\left[\begin{array}{ccc}1& -1& 2\\ 2& 1& 3\\ 3& 2& 4\end{array}\right]$ into an upper triangular matrix by using the suitable column transformations.

Show that matrices $A$ and $B$ are row equivalent if $A=\left[\begin{array}{ccc}1& -1& 0\\ 2& 1& 1\end{array}\right]$ and $B=\left[\begin{array}{lll}3& 0& 1\\ 0& 3& 1\end{array}\right]$.

Transform $\left[\begin{array}{ccc}1& 2& 3\\ 2& 5& 7\\ 3& 1& 2\end{array}\right]$ into an upper triangular matrix by using the suitable row transformations.

For the following equations 

$x+3y+3z=12$

$x+4y+4z=15$

$x+3y+4z=13$

Using the method of reduction. Select the correct options.

Transform $\left[\begin{array}{ccc}1& -1& 2\\ 2& 1& 3\\ 3& 2& 4\end{array}\right]$ into an upper triangular matrix by suitable column transformations.
 

Convert $\left[\begin{array}{cc}1& -1\\ 2& 3\end{array}\right]$ into an identity matrix by suitable row transformations. 
 

Use suitable transformation on $\left[\begin{array}{cc}1& 2\\ 3& 4\end{array}\right]$ to convert it into an upper triangular matrix.

Find the addition of two new matrices $A=\left[\begin{array}{ccc}1& -1& 3\\ 2& 1& 0\\ 3& 3& 1\end{array}\right], C_3\to C_3+2C_2$ and then $3R_{3 }.$

Find the addition of the two new matrices. 

$A=\left[\begin{array}{ccc}1& -1& 3\\ 2& 1& 0\\ 3& 3& 1\end{array}\right], 3R_3$ and then $C_3\to C_3+2C_2.$

What do you observe? 

$A=\left[\begin{array}{ccc}1& 2& -1\\ 0& 1& 3\end{array}\right],2C_2$ and $B=\left[\begin{array}{ccc}1& 0& 2\\ 2& 4& 5\end{array}\right] ,-3R_1.$

Apply the given elementary transformation on the following matrix $A=\left[\begin{array}{cc}5& 4\\ 1& 3\end{array}\right],C_1\leftrightarrow C_2; B=\left[\begin{array}{cc}3& 1\\ 4& 5\end{array}\right],R_1\leftrightarrow R_2.$

Apply the given elementary transformation on the following matrix $B=\left[\begin{array}{ccc}1& -1& 3\\ 2& 5& 4\end{array}\right],R_1\to R_1-R_{2.}$

Apply the given elementary transformation on the following matrix. $A=\left[\begin{array}{cc}1& 0\\ -1& 3\end{array}\right],R_1\leftrightarrow R_{2.}$

If $A=\left[\begin{array}{ccc}2& 1& 3\\ 1& 0& 1\\ 1& 1& 1\end{array}\right]$ then reduce it to $I_3$ by using row transformations.