Let 
be the set of all 3×3 symmetric matrices whose entries are 1,1,1,0,0,0,–1, –1, –1. B is one of the matrix in set 
and
X = 
U = 
V = 
.
(i) Number of such matrices B in set 
is λ , then λ lies in the interval
Text Solution
Verified by Experts(i)(a,c); (ii)(a,c); (iii)(a,c)
(i)(a,c) Let any symmetric matrix B = 
so total matrices possible = 3 ! × 3 ! = 36.
(ii)(a,c) For homogeneous system infinite solution are possible if |B| = 0
|B| = abc + 2xyz – by 2 – cx 2 – az 2.
abc = xyz = 0 (one of a,b,c and one of x, y, z is zero)
if a = 0 z = 0 ⇒ |B| = 0 - 4 cases
b = 0 y = 0 ⇒ |B| = 0 - 4 cases
c = 0 x = 0 ⇒ |B| = 0 - 4 cases
so total cases are 12.
(iii)(a,c) BX = V is always inconsistent. when |B| = 0
so 12 cases
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