If A= [ array lll 1 & 2 & 3 1 & 1 & a 2 & 4 & 7 array ] and B= [ array ccc 13 & 2 & b -3 & -1 & 2 -2 & 0 & 1 array ] where matrix B is inverse of matrix a , then the value of a and b are

Step-by-step solution

A= | array lll 1 & 2 & 3 1 & 1 & a 2 & 4 & 7 array |=(7-4 a)-2(7-2 a)+3(2)=-1 matrix B is inverse of matrix A. ' b ' is element (1 3) in matrix B. Here element (3 1) in matrix A is 2 . Cofactor of 2==(-1)³⁺¹ | array ll 2 & 3 1 & a array |=2 a -3 Now 2 a -3 -1 = b 2 a + b =3 For element (1 2) in matrix A i.e. 2 Now cofactor of 2 is (-1)¹⁺² | array ll 1 & a 2 & 7 array |=-(7-2 a) and -(7-2 a ) -1 =7-2 a Here element (2 1) in matrix B is -3 7-2 a =-3 Solving eq. (1) and (2), we get a =5, ~b =-7