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 _________.

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 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=0 (C) ab+bc+ca=1 (D) ab+bc+ca=0

The greatest value of c in R 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

If [(a,b),(c,-a)] is a square root of the 2xx2 identity matrix then a,b,c satisfy the relation (A) 1-a^2-bc=0 (B) 1-a^2+bc=0 (C) 1+a^2-bc=0 (D) 1+a^2+bc=0

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

The function f(x)=(a sin x+b cos x)/(c sin x+d cos x) is decreasing,if (i) ad-bc>0 (ii) ad-bc 0 (ii) ab-dc<0