The system of linear equations `ax+by=0,cx+dy=0` has a non trivial solution if (A) `ad+bc=0` (B) `ad-bc=0` (C) `ad-bc,0` (D) `ad-bc.0`

The system of equations ax + 4y + z = 0,bx + 3y + z = 0, cx + 2y + z = 0 has non-trivial solution if a, b, c are in

The greatest value of for which the system of linear equations x-cy-cz=0 cx-y+cz=0 cx+cy-z=0 Has a non-trivial solution, is 1/k . The value of k is _________.

The value of a for which the system of linear equations ax+y+z=0, ay+z=0,x+y+z = 0 possesses non-trivial solution is

if a gt b gt c and the system of equations ax + by + cz = 0, bx + cy + az 0 and cx + ay + bz = 0 has a non-trivial solution, then the quadratic equation ax^(2) + bx + c =0 has

If the system of equation ax + by + cz = 0, bx + cy + az = 0, cx + ay + bz = 0 has non-trivial solution then find the value of |{:(bc-a^2,ca-b^2,ab-c^2),(ca-b^2, ab-c^2, bc-a^2),(ab-c^2, bc-a^2, ca-b^2):}|

If a gt b gt c and the system of equtions ax +by +cz =0 , bx +cy+az=0 , cx+ay+bz=0 has a non-trivial solution then both the roots of the quadratic equation at^(2)+bt+c are

if the system of equations (a-t)x+by +cz=0 bx+(c-t) y+az=0 cx+ay+(b-t)z=0 has non-trivial solutions then product of all possible values of t is

If the lines ax+by+c=0, bx+cy+a=0 and cx+ay+b=0 (a, b,c being distinct) are concurrent, then (A) a+b+c=0 (B) a+b+c=1 (C) ab+bc+ca=1 (D) ab+bc+ca=0

If the system of linear equations ax +by+ cz =0 cx + ay + bz =0 bx + cy +az =0 where a,b,c, in R are non-zero and distinct, has a non-zero solution, then:

If the equation x^2+ax+bc=0" and " x^2-bx+ca=0 have a common root, then a+b+c =