Evaluate: ` [[x,y,x+y],[y,x+y,x],[x+y,x,y]]`

The determinant [[x,y,x+y],[y,x+y,x],[x+y,x,y]] is divisible by

Evaluate det[[x,y,x+yy,x+y,xx+y,x,y]]

Evaluate det[[1,x,y1,x+y,y1,x,x+y]]

Using properties of determinants , find the value of k if |{:(x,y,x+y),(y,x+y,x),(x+y,x,y):}|=k(x^(3)+y^(3)) .

Using properties of determinants, prove the following |[x,x+y,x+2y],[x+2y,x,x+y],[x+y,x+2y,x]|=9y^2(x+y)

Evaluate: (i) |(x^2+x y+y^2,x+y ),(x^2-x y+y^2,x-y)| (ii) |(1,(log)_b a),((log)_a b,1)|

Evaluate the following: |[1,x,y],[1, x+y, y],[1, x, x+y]|

evaluate: |(a+x,y,z),(x,a+y,z),(x,y,a+z)|

evaluate: |(3x,-x+y,-x+z),(x-y,3y,z-y),(x-z,y-z,3z)|