question_answer 67)

Solve the system of equations using matrix method x – y + z = 4 2x + y – 3z = 0 x + y + z = 2  

Answer:

The given system of equations can be expressed as AX = B, where             and             = 1 (1 + 3) + 1 (2 + 3) + 1 (2 ? 1)             = 4 + 5 + 1 = 10  0       Therefore A is non-singular matrix so A?1 exists and given system has unique solution.                 A11 = 4; A12 = ?5; A13 = 1       A21 = 2; A22 = 0; A23 = ?2       A31 = 2; A32 = 5; A33 = 3       adj                           Now AX = B                         On equating, we get x =2, y = ?1, z = 1.