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

Step-by-step solution

aligned & We have A [ array cc 5 a & - b 3 & 2 array ] and A adj A = AA ^ T & [ 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 & 10 a +3 ~b array ]= [ array cc 25 a ^2+ b ^2 & 15 a -2 ~b 15 a -2 ~b & 9+4 array ] & 10 a +3 ~b =13 and 15 a -2 ~b =0 aligned Solving these equations, we get a= 2 5 and b=3 5 a+b=2+3=5