If the matrix A = [ array cc 1 & 2 -5 & 1 array ] and A ⁻¹=x ~A +y I , when I is a unit matrix of order 2 , then the value of 2 x+3 y is

Step-by-step solution

aligned & A = [ array cc 1 & 2 -5 & 1 array ] & A =11 & ~A ⁻¹= 1 | ~A | [ array cc 1 & -2 5 & 1 array ]= 1 11 [ array cc 1 & -2 5 & 1 array ] & A ⁻¹=x ~A +y I , we get & [ array cc 1 11 & -2 11 5 11 & 1 11 array ]= [ array cc x & 2 x -5 x & x array ]+ [ array ll y & 0 0 & y array ] aligned array ll & [ array cc 1 11 & -2 11 5 11 & 1 11 array ]= [ array cc x+y & 2 x -5 x & x+y array ] & x= -1 11 and y= 2 11 & 2 x+3 y=2 ( -1 11 )+3 ( 2 11 )= 4 11 array