|[a,b,c],[a+2x,b+2y,c+2z],[x,y,z]|=0

prove that abs[[a,b,c],[a+2x,b+2y,c+2z],[x,y,z]]=0

Show without expanding at any stage that: det [ [a,b,c],[a+2x,b+2y,c+2z],[x,y,z]] =0

Show that abs((a,b,c),(a+2x,b+2y,c+2z),(x,y,z)) =0

If x ,y ,z are different from zero and "Delta"=|[a, b-y ,c-z],[ a-x, b ,c-z],[ a-x, b-y, c]|=0, then the value of the expression a/x+b/y+c/z is a. 0 b. -1 c. 1 d. 2

If x ,y ,z are different from zero and "Delta"=|[a, b-y ,c-z],[ a-x, b ,c-z],[ a-x, b-y, c]|=0, then the value of the expression a/x+b/y+c/z is a. 0 b. -1 c. 1 d. 2

If x ,y ,z are different from zero and "Delta"=|[a, b-y ,c-z],[ a-x, b ,c-z],[ a-x, b-y, c]|=0, then the value of the expression a/x+b/y+c/z is 0 b. -1 c. 1 d. 2

If x ,y ,z are different from zero and "Delta"=|[a, b-y ,c-z],[ a-x, b ,c-z],[ a-x, b-y, c]|=0, then the value of the expression a/x+b/y+c/z is 0 b. -1 c. 1 d. 2

Show that |a b c a+2x b+2y c+2z x y z|=0

Show that |a b c a+2x b+2y c+2z x y z|=0

By using properties of determinants. Show that: (i) |[a-b-c,2a,2a],[2b,b-c-a,2b],[2c,2c,c-a-b]|=(a+b+c)^3 (ii) |[x+y+2z, x, y],[ z, y+z+2x, y],[ z, x, z+x+2y]|=2(x+y+z)^3