If $\mathrm{A}=\left[\begin{array}{cc}-5& -3\\ 2& 1\end{array}\right]$ , then ${\mathrm{A}}^{-1}=$ _____.

The solution of the system of linear equations $\mathrm{x}+\mathrm{y}=2, 4\mathrm{x}+\mathrm{y}=6$ is _____.

What is the solution for following system of linear equations?

2x + 3y - 5 = 0, 4x + 6y - 7 = 0.

What is the solution of following system of linear equations?

$\mathrm{x}+2\mathrm{z}=9, 4\mathrm{x}+2\mathrm{y}+\mathrm{z}=14, \mathrm{x}+3\mathrm{y}+4\mathrm{z}=26$ .

What is the solution of following system of linear equations?

$\mathrm{x}+2\mathrm{y}=3, 2\mathrm{x}+3\mathrm{y}=5$ .

The matrix $\mathrm{A}=\left[\begin{array}{cccc}1& 0& 4& 6\\ 0& 1& 5& 7\\ 0& 0& 0& 1\end{array}\right]$ is in

Let $\mathrm{A}=\left[\begin{array}{ccc}1& 2& 2\\ 0& 2& 1\\ -1& 2& 2\end{array}\right]$ . Then $\mathrm{\rho }\left({\mathrm{A}}^{\mathrm{T}}\right)=$ _____.

The system of simultaneous linear equations  $\mathrm{x}+2\mathrm{y}+3\mathrm{z}=5, \mathrm{x}+\mathrm{y}+4\mathrm{z}=10, 2\mathrm{x}+2\mathrm{y}+8\mathrm{z}=\mathrm{\mu }$ will have infinitely many solutions for $\mathrm{\mu }$ equals to _____.

If $\mathrm{\rho }\left(\mathrm{A}\right)\ne \mathrm{\rho }\left(\mathrm{A}|\mathrm{B}\right)$ , then the system _____.

For a system of linear equations, $\left[\mathrm{A}:\mathrm{B}\right]=\left[\begin{array}{ccccc}1& 2& 3& :& 4\\ 2& -1& -2& :& {\mathrm{a}}^2\\ -1& -7& -11& :& \mathrm{a}\end{array}\right]$ is an augmented matrix and $\mathrm{a}\in \mathrm{ℝ}$. Then for what values of $\mathrm{a}$ the corresponding system is consistent?