Question

The system of equations
2x+6y+11=0,6y-18z +1 = 0
6x + 20y - 6z + 3 = 0
1) is consistent 2) has unique solution
3) is inconsistent 4) cannot be determined​

Answer 1

Answer:

The given system of equations can be written as AX=B

where A=

⎣

⎢

⎢

⎡

2

0

6

6

6

20

0

−18

−6

⎦

⎥

⎥

⎤

, X=

⎣

⎢

⎢

⎡

x

y

z

⎦

⎥

⎥

⎤

,B=

⎣

⎢

⎢

⎡

−11

−1

−3

⎦

⎥

⎥

⎤

Here, D=∣A∣=

∣

∣

∣

∣

∣

∣

∣

∣

2

0

6

6

6

20

0

−18

−6

∣

∣

∣

∣

∣

∣

∣

∣

D=0

Now, D

1

=

∣

∣

∣

∣

∣

∣

∣

∣

−11

−1

−3

6

6

20

0

−18

−6

∣

∣

∣

∣

∣

∣

∣

∣

⇒D

1

=−3276



=0

As, D=0 and at least one of D

1

,D

2

,D

3

is non-zero, the system of equation is inconsistent and has no solution.

Hence, option 'C' is correct.

Answer 2

Answer:

Step-by-step explanation: