If A= [ array lll a & 1 & 2 1 & 2 & b c & 1 & 3 array ] and Adj A= [ array ccc 7 & -1 & -5 -3 & 9 & 5 1 & -3 & 5 array ] then a^2+b^2+c^2=

Step-by-step solution

A= | array lll a & 1 & 2 1 & 2 & b c & 1 & 3 array |, Adj A= | array ccc 7 & -1 & -5 -3 & 9 & 5 1 & -3 & 5 array | We know, Adj A= | array lll c₁₁ & c₂₁ & c₃₁ c₁₂ & c₂₂ & c₃₂ c₁₃ & c₂₃ & c₃₃ array | Where, c _ ij is co-factor of a _ ij Now, c ₁₁=7 | array ll 2 & b 1 & 3 array |=7 6-b=7 b=-1 Also, c ₁₃=1 | array ll 1 & 2 c & 1 array |=1 1-2 c =1 c =0 and, c₃₃=5 | array ll a & 1 1 & 2 array |=5 2 a -1=5 a =3 So, a^2+b^2+c^2=9+1+0=10