If A= [ array cc 5 a & -b 3 & 2 array ] and A adj A=A^T , then 5 a + b is equal to

Step-by-step solution

aligned & A ₁₁=(-1)¹⁺¹(2)=2, ~A ₁₂=(-1)¹⁺²(3)=-3 & ~A ₂₁=(-1)²⁺¹(- b )= b , A ₂₂=(-1)²⁺²(5 a )=5 a aligned adj A= [ array cc 2 & -3 b & 5 a array ]^T= [ array cc 2 & b -3 & 5 a array ] Given, A adj A = AA ^ T aligned & [ array cc 5 a & - b 3 & 2 array ] [ array cc 2 & ~b -3 & 5 a array ]= [ array cc 5 a & - b 3 & 2 array ] [ array cc 5 a & 3 - b & 2 array ] & [ array cc 10 a +3 ~b & 0 0 & 3 ~b +10 a array ]= [ array cc 25 a ^2+ b ^2 & 15 a -2 ~b 15 a -2 ~b & 13 array ] aligned by the equality of matrices, array ll