Question

1.3) Examine the consistency of the following equations. i) 2r-y+3 = 0, 3x+y-2=0, 11x+2y-3 = 0)​

Answer 1

Answer:

2x+6y+11=0

6x+20y−6z+3=0

6y−18z+1=0

Converting above equations in the determinant form, we get

Δ=

∣

∣

∣

∣

∣

∣

∣

∣

2

6

0

6

20

6

0

−6

−18

∣

∣

∣

∣

∣

∣

∣

∣

Here, Δ=−648+648=0

Now,

Δ

1

=

∣

∣

∣

∣

∣

∣

∣

∣

−11

−3

−1

6

20

6

0

−6

−18

∣

∣

∣

∣

∣

∣

∣

∣

Δ

1

=3276



=0

Δ

2

=

∣

∣

∣

∣

∣

∣

∣

∣

2

6

0

−11

−3

−1

0

6

−18

∣

∣

∣

∣

∣

∣

∣

∣

Δ

2

=−1092



=0

And Δ

3

=

∣

∣

∣

∣

∣

∣

∣

∣

2

6

0

6

20

6

−11

−3

−1

∣

∣

∣

∣

∣

∣

∣

∣

Δ

3

=−364



=0

So, here D=0 and no-one among D

1

,D

2

,D

3

is 0.

Hence, the system is inconsistent

Hence, option C.