List of top Mathematics Questions on System of Linear Equations asked in AP EAPCET

Consider the system of linear equations \[ x+y+z=6, \] \[ x+2y+3z=10, \] \[ 3x+2y+\lambda z=\mu. \] If the system has infinitely many solutions, then the value of \(\mu+\lambda\) is:

If the system of linear equations $x + y + z = 1$, $x + 2y + 4z = \eta$, $x + 4y + 10z = \eta^2$ has a solution, then the value of $\eta$ is:

The rank of the matrix \[ A= \begin{bmatrix} 2 & 1 & 2 \\ 1 & 0 & 1 \\ 4 & 1 & 4 \end{bmatrix} \] is

If the system of simultaneous linear equations \(x+y-z=6\), \(3x-y+z=2\) and \(x+ky+z=-8\) has a unique solution \(x=2\), \(y=\beta\), \(z=\gamma\), then the value of \(k\) satisfies the following quadratic equation:

If the system of simultaneous linear equations \[ 3x-4y+kz+13=0,\quad x+2y-z-9=0 \] \[ kx-y+3z+7=0 \] has a unique solution \(x=\alpha,\ y=\beta,\ z=\gamma\) for \(k\neq m\) and \(2\beta-\gamma=8\), then \(\alpha+m=\)

If the solution of the system of simultaneous equations \[ \frac{1}{x}+\frac{2}{y}-\frac{3}{z}-1=0, \] \[ \frac{2}{x}-\frac{4}{y}+\frac{3}{z}-1=0 \] and \[ \frac{3}{x}+\frac{6}{y}-\frac{6}{z}-4=0 \] is \(x=\alpha,\ y=\beta,\ z=\gamma\), then \(\alpha^2+\gamma^2=\)