MATHEMATICS-2

Que 4 : Show that the equations
2x+6y=-11,
6x+20y-6z=-3,
6y-18z=-1
are not consistent.

Solution :

which gives
2x + 6y + 0z =-11
0x + 2y-6z = 30
0x + 0y + 0z = -91
The last equation shows that given system of equations is inconsistent. In this problem, we observe that the rank of coefficient matrix A is 2 as it has only two non-zero rows. Whereas rank of [A|B] is 3. Since it has three nonzero rows. Thus p(A) != P[A|B]
Hence, we infer that if in the matrix equation AX=B, rank of A and [A|B] are unequal the given system of equations is not consistent. Proved