Question

If the system of equations: 2x+3y-z=0 3x+2y+kz=0 4x+y+z=0have a set of non-zero integral solutions then, find the smallest positive value of z..

Answer 1

Answer:

2x+3y−z=0

3x+2y+kz=0

4x+y+z=0

⎣

⎢

⎢

⎡

0

0

0

⎦

⎥

⎥

⎤

=

⎣

⎢

⎢

⎡

2

3

4

3

2

1

−1

k

1

⎦

⎥

⎥

⎤

......[CRAMER’S RULE]

Δ=2(2−K)−3(3−4K)−1(3−8)

=4−2K−9+12K+5

=10K

Now, x=

△

△

1

,y=

△

△

2

,z=

△

△

3

Clearly, △

1

=△

2

=△

3

=0

⇒K



=0

⇒x=y=z=0, which is not possible.

Answer 2

Answer:

thankyou thankyou thankyou thankyou