The number of solution of equations x2-x3=1, -x1+2x3=2, x1-2x2=3 is (1) zero - Maths - Determinants

Question

The number of solution of equations x 2 - x 3 = 1 ,   - x 1 +
2 x 3 = 2 ,   x 1 - 2 x 2 = 3   is
(1) zero (2) one (c) two (d) infinite

Neha Bhateja · Accepted Answer

Dear student,

The given system of equation is

0x1 + x2-x3=1-x1+0x2 + 2x3=2x1-2x2 + 0x3=3

Now, from Cramer's rule
â€‹
D=01-1-1021-20=00+4 - 10-2 - 12-0=0 + 2 - 2=0

D1=11-12023-20==10+4 - 10-6 - 1-4-0=4+6+4=14

Now, by Cramer,s rule

If D=0  any one of D1 , D2 and D3 not
equal to zero

then system of equation has no solution

so answer will be (A)

Regards

The number of solution of equations x 2 - x 3 = 1 , - x 1 + 2 x 3 = 2 , x 1 - 2 x 2 = 3 is (1) zero (2) one (c) two (d) infinite