List of top Mathematics Questions on Solutions of Linear Algebraic Equations

If $x=\alpha$, $y=\beta$, $z=\gamma$ satisfy the equations \[ 3x+y+2z+2=0, \] \[ 2x-3y+z-7=0, \] \[ x-4y+3z-1=0, \] then \[ \alpha^3-\beta^3= \]

If the two systems of equations \( x+y-2z=0, 4x+4y-8z=0, 3x+3y-6z=0 \) and \( x+y+z=3, 2x+2y-z=\lambda, x+y-\mu z=1 \) have the same set of solutions, then \( \lambda+\mu = \)

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: