Paragraph: Let A be the set of all 3 3 symmetric matrices all of whose entries are either 0 or 1 . Five of these entries are 1 and four of them are 0 . Question: The number of matrices A in A for which the system of linear equations A [ array l x y z array ]= [ array l 1 0 0 array ] is is inconsistent, is

Step-by-step solution

Given, A [ array l x y z array ]= [ array l 1 0 0 array ] Case I [ array lll 1 & a & b a & 1 & c b & c & 1 array ] [ array l x y z array ]= [ array l 1 0 0 array ]a, b, c are selected from 1,0,0 . x+a y+b z=1 a x+y+c z=0b x+c y+z=0 (i) If a=1, b=c=0 , then x+y=1 Inconsistent system of equation x+y=0 (ii) If a=0=c, b=1 , then x+z=1 , y=0 Inconsistent system of equation x+z=0 (iii) If c=1, a=b=0 , then x=1, z=0 , y=0 Case II (i) [ array lll 1 & a & b a & 0 & c b & c & 0 array ] [ array l x y z array ]= [ array l 1 0