Evaluate `|{:(1,x,y),(x,x+y,y),(1,x,x+y):}|`

Evaluate |[1,x, y],[1,x+y, y],[1,x,x+y]|

Find the value of the "determinant" |{:(1,x,y+z),(1,y,z+x),(1,z,x+y):}|

Evaluate |(x, y, x+y),( y, x+y, x),( x+y, x, y)| .

Evaluate: (i) |(x^2+x y+y^2,x+y ),(x^2-x y+y^2,x-y)|

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

Evaluate x and y if [(x,2),(-3,y)]=2[(x^(2),1),(-(3)/(2),3y-5)] .

Find x and y, if : [{:(,x,3x),(,y,4y):}] [{:(,2),(,1):}]=[{:(,5),(,12):}]

If the points (x_1, y_1),(x_2,y_2), and (x_3, y_3) are collinear show that (y_2-y_3)/(x_2x_3)+(y_3-y_1)/(x_3x_1)+(y_1-y_2)/(x_1x_2)=0

(1)/((x)/(y)+(y)/(x))=

If |(x, x-y),(2x+y,7)|=|(3, 1),( 8, 7)| , then find the value of y