Let Z = 18 + 26i where `Z_0 = x_0 + iy_0 (x_0, y_0 in" R")` is the cube root of Z having least positive argument. Find the value of `x_0y_0(x_0 + y_0).`

Write the number of solution of the following system of equation.x+y-z=0 3x-y+z=0 x-3y+z=0

The number of non-trivial solutions of the system x=y+z=0, x+2y-z=0, 2x+y+3z=0 , is

If (x_(0), y_(0), z_(0)) is any solution of the system of equations 2x-y-z=1, -x-y+2z=1 and x-2y+z=2 , then the value of (x_(0)^(2)-y_(0)^(2)+1)/(z_(0)) (where, z_(0) ne 0 ) is

If (x_(0), y_(0), z_(0)) is any solution of the system of equations 2x-y-z=1, -x-y+2z=1 and x-2y+z=2 , then the value of (x_(0)^(2)-y_(0)^(2)+1)/(z_(0)) (where, z_(0) ne 0 ) is

if the system of equations x+y+z=0 , x+3y+k^2z=0 and x+2y+z=0 have a non zero solution then value of y+(x/z) is

If x, y, z are non zero real numbers, then find the inverse of matrix A=[[x, 0, 0],[ 0, y, 0],[ 0, 0, z]] .

The plane x =0, x =a, y =0, y =a , z = and z =a from a

If the system of equations x+a y=0, a z+y=0 and a x+z=0 has infinite solutions, then the value of a is