Solve :`|(x + a, b, c),(a, x+b, c),(a, b, x + c)|`=0

The product of all values of t , for which the system of equations (a-t)x+b y+c z=0,b x+(c-t)y+a z=0,c x+a y+(b-t)z=0 has non-trivial solution, is (a) |[a, -c, -b], [-c, b, -a], [-b, -a, c]| (b) |[a, b, c], [b, c, a], [c, a, b]| (c) |[a, c, b], [b, a, c], [c, b, a]| (d) |[a, a+b, b+c], [b, b+c, c+a], [c, c+a, a+b]|

Solve the equation |[a-x, c, b], [ c, b-x, a], [b, a, c-x]|=0 where a+b+c!=0.

One root of the equation |(x+a,b,c),(b,x+c,a),(c,a,x+b)|=0 is -

|{:(a-x," "b," "c),(" "b,c-x," "a),(" "c," "a,b-x):}|=0

If a+b+c=0, one root of [[a-x, c, b],[c, b-x, a],[ b, a, c-x]]=0 is a. x=1 b. x=2 c. x=a^2+b^2+c^2 d. x=0

Prove that (a+b+c+x) is a factor of |(x+a, b,c),(b,x+c,a),(c,a,x+b)|

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 |(0,x-a,x-b),(x+a,0,x-c),(x+b,x+c,0)|=0 then the value of x is -

If x+y+z=0 prove that |[a x, b y, c z],[ c y, a z ,b x],[ b z ,c x ,a y]|=x y z|[a, b, c],[c ,a ,b],[b ,c ,a]|

Prove that |[a x-b y-c z, a y+b x, c x+a z], [a y+b x, b y-c z-a x, b z+c y],[c x+a z, b z+c y, c z-a x-b y]|=(x^2+y^2+z^2)(a^2+b^2+c^2)(a x+b y+c z)dot