Find the determinate of
(X + z X X3
Z + X Y Y3
X + Y Z Z3)
The determinate of a 3x3 matrix is calculated as follows:
det = X(Y*Z3 - Y3*Z) - X*(Z*Y3 - Z3*Y) + X3(Z*Y - Z3*Y)
Therefore, the determinate of the given matrix is:
det = X(Y*Z3 - Y3*Z) - (Z*Y3 - Z3*Y) + X3(Z*Y - Z3*Y)
det = X(Y*Z3 - Y3*Z) - Z*Y3 + Z3*Y + X3(Z*Y - Z3*Y)
det = X(YZ3 - Y3Z) - ZY3 + Z3Y + X3ZY - X3Z3Y
det = XYZ3 - XY3Z - ZY3 + Z3Y + X3ZY - X3Z3Y
det = XYZ3 - XYZ3 + Z3Y - ZY3 + X3ZY - X3Z3Y
det = Z3Y - ZY3 + X3ZY - X3Z3Y
det = 3ZY - 3ZY
det = 0
Therefore, the determinate of the given matrix is 0.