Elementary Transformations of a Matrix

Find the rank of the matrix $A=\left[\begin{array}{cccc}1& -1& 2& -3\\ 4& 1& 0& 2\\ 0& 3& 0& 4\\ 0& 1& 0& 2\end{array}\right]$

If $AX=B$, where $A=\left[\begin{array}{ccc}1& -1& 1\\ 2& 1& -3\\ 1& 1& 1\end{array}\right]$,$X=\left[\begin{array}{c}x\\ y\\ z\end{array}\right],B=\left[\begin{array}{c}4\\ 0\\ 2\end{array}\right]$, then $2x+y-z=$

Rank of the matrix $\left[\begin{array}{ccc}1& -2& 3\\ 2& 4& -6\\ 5& 1& -1\end{array}\right]$ is

What is the minimum number of elementary operations that are needed to transform $A=\left[\begin{array}{cc}0& 1\\ 1& 2\end{array}\right]$ to the identity matrix?

Reduce the matrix $\left[\begin{array}{cccc}2& -2& 4& 3\\ -3& 4& -2& -1\\ 6& 2& -1& 7\end{array}\right]$ to a row-echelon form.

Reduce the matrix $\left[\begin{array}{cccc}0& 3& 1& 6\\ -1& 0& 2& 5\\ 4& 2& 0& 0\end{array}\right]$ to a row-echelon form.

Reduce the matrix $\left[\begin{array}{ccc}3& -1& 2\\ -6& 2& 4\\ -3& 1& 2\end{array}\right]$ to a row-echelon form.

If the rank of the matrix $\left(\begin{array}{ccc}\lambda & -1& 0\\ 0& \lambda & -1\\ -1& 0& \lambda \end{array}\right)$ is $2$, then $\lambda$ is

Which of the following matrix has rank $3 ?$

What is the rank of the matrix $\left[\begin{array}{lll}1& 1& 1\\ 1& 1& 1\\ 1& 1& 1\end{array}\right]=?$

Given that $\left(\begin{array}{cc}9& 6\\ 3& 0\end{array}\right)=\left(\begin{array}{cc}2& 3\\ 1& 0\end{array}\right)\left(\begin{array}{cc}3& 0\\ 1& 2\end{array}\right)$. Applying elementary row transformation $R_1\to R_1–2 R_2$ on both sides, we get

On using elementary column operations $C_2\to C_2-2C_1$ in the following matrix equation $\left[\begin{array}{cc}1& -3\\ 2& 4\end{array}\right]=\left[\begin{array}{cc}1& -1\\ 0& 1\end{array}\right]\left[\begin{array}{cc}3& 1\\ 2& 4\end{array}\right]$ , we have

On using elementary row operation $R_1\to R_1-3R_2$ in the following matrix equation $\left[\begin{array}{ll}4& 2\\ 3& 3\end{array}\right]=\left[\begin{array}{ll}1& 2\\ 0& 3\end{array}\right]\left[\begin{array}{ll}2& 0\\ 1& 1\end{array}\right]$, we have

Find the rank of the $\left[\begin{array}{cccc}3& -8& 5& 2\\ 2& -5& 1& 4\\ -1& 2& 3& -2\end{array}\right]$ by row reduction method.

Find the rank of the matrix by minor method: $\left[\begin{array}{ccc}1& -2& 3\\ 2& 4& -6\\ 5& 1& -1\end{array}\right]$

Find the rank of the matrix by minor method: $\left[\begin{array}{cc}2& -4\\ -1& 2\end{array}\right]$.

The rank of the matrix $\left[\begin{array}{cccc}1& 2& 3& 4\\ 2& 4& 6& 8\\ -1& -2& -3& -4\end{array}\right]$ is

By using elementary transformations, find the inverse of the matrix $A=\left[\begin{array}{ll}1& 3\\ 2& 7\end{array}\right]$.

Solve the following system of linear equations by matrix method.

$x-y+2z=7$

$3x+4y-5z=-5$

$2x-y+3z=12$