For what value of k do the following system of equations possess a non trivial (i.e. not all zero) solutions over the set of rationales Q? IIT JEE 1979 + ky 3z-0 3x+ky-223: 0 For the non trivial solution D 0 1(-4k 6) k(-12 4) +3(9 - 2k)0 -2k +330 k 33
If A and B are square matrices of equal degree, then which one is correct among the IITTEE following? 1995 (a) A+B B+ A (c) A B B A (b) A + B A-B (d) AB BA If A and B are square matrices of same degree then matrices Aand B can be added or subtracted or multiplies. By algebra of matrices the only correct option is A B B A.
Let a, b, c be the real numbers. The following system of equations in x,-y and z 1995 (a) no solution (c) infinitely many solution (b) unique solution (d) finitely many solution The given system of equations becomes . New system of equations has unique solution 1 1-1 For the new system, we have D3 1 -1 1 1-1 1) 1(1 1)1(1-1)-4 Now, x =-=-= 1 D2 D4
if (co # 1) is a cube root of unity, then 1995 -i -i+ -1-1 (a) o (b) 1 (c) i (d) a) Operating R1R12 + R3 =11-i -1 =0