Question

Solve by matrix inversion method:

(i) x – y + 2z = 3; 2x + z = 1; 3x + 2y + z = 4 

(ii) 2x – z = 0; 5x + y = 4; y + 3z = 5

Answer 1

(i) The given system can be written as

= 1(0 – 2) – (-1)(2 – 3) + 2(4 – 0) 

= -2 – (-1)(-1) + 2(4) 

= -2 – 1 + 8 

= 5

∴ adj A 

x = -1, y = 2, z = 3.

(ii) The given system can be written as

= 2(3 – 0) – 0(15 – 0) – 1(5 – 0) 

= 2(3) – 0(15) – 1(5)

= 6 – 0 – 5 

= 1

∴ x = 1, y = -1, z = 2.