System of Linear Equations

Using matrices, solve the following system of equations

 $\begin{array}{l}4x-5y-11z=12\end{array}$

$x-3y+z=1$

$2x+3y-7z=2$

Find the rank of $\left[\begin{array}{cccc}2& -1& 3& 4\\ 0& 3& 4& 1\\ 2& 3& 7& 5\\ 2& 5& 11& 6\end{array}\right]$.

Solve the given system of equations using the inverse of a matrix.

$\begin{array}{r}x+2y=5\\ x+3y=7\end{array}$

Solve the given system of equations using the inverse of a matrix.

$\begin{array}{r}3x+8y=5\\ 4x+11y=7\end{array}$

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: $\left[\begin{array}{cc}2& -4\\ -1& 2\end{array}\right]$.

If $0\le \theta \le \pi$ and the system of equations $x+\left(\sin \theta \right)y-\left(\cos \theta \right)z=0, \left(\cos \theta \right)x-y+z=0, \left(\sin \theta \right)x+y-z=0$ has a non-trivial solution then $\theta$ is

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

Determine the value of $\lambda$ for which the following system of equation has a non-trival solution $x+y+3z=0, 4x+3y+\lambda z=0, 2x+y+2z=0$

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 row transformations.