question_answer 69)

Solve the system of equations using matrix method x – y + 2z = 7; 3x + 4y – 5z = –5; 2x – y + 3z = 12.  

Answer:

The given system of equations can be expressed as       AX = B, where                                 and               = 1 (12 ? 5) + 1(9 + 10) + 2 (?3 ? 8)       = 7 + 19 ? 22 = 4 0       Therefore A is non-singular matrix so A?1 exists and given system has a unique solution.       A11 = 7; A12 = ?19; A13 = ?11       A21 = 1; A22 = ?1; A23 = ?1       A31 = ?3; A32 = 11; A33 = 7                               Now                         On equating, we get x = 2, y = 1 and z = 3.