Question

a) 2x-2y-5z=0 ; 4x-y+z=0 ; 3x-2y+3z=0 by reduction method

Answer 1

Answer:

MATHS

If the system of equations x+y+z=5, x+2y+3z=9, x+3y+αz=β has infinitely many solutions, then β−α equals?

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ANSWER

D=

∣

∣

∣

∣

∣

∣

∣

∣

1

1

1

1

2

3

1

3

α

∣

∣

∣

∣

∣

∣

∣

∣

=

∣

∣

∣

∣

∣

∣

∣

∣

1

0

0

1

1

2

1

2

α−1

∣

∣

∣

∣

∣

∣

∣

∣

=(α−1)−4=(α−5)

for infinite solutions D=0⇒α=5

D

x

=0⇒

∣

∣

∣

∣

∣

∣

∣

∣

5

9

β

1

2

3

1

3

5

∣

∣

∣

∣

∣

∣

∣

∣

=0

⇒

∣

∣

∣

∣

∣

∣

∣

∣

0

−1

β−15

0

−1

−2

1

3

5

∣

∣

∣

∣

∣

∣

∣

∣

=0

⇒2+β−15=0

⇒β−13=0

on β=13 we get D

y

=D

z

=0

α=5,β=13.