Question

the system of linear equations x+3y+((lambda)+2)z=0, 2x+4y+8z=0, 3x+5y+10z=0 has non-trivial solution, when lambda is

Answer 1

Answer:

Lamda(x)=10

Step-by-step explanation

$\left[\begin{array}{ccc}1&3&x+2\\2&4&8\\3&5&10\end{array}\right]$ = 0

on solving X=2

Answer 2

Answer:

The value of lambda for which the system of solutions will have a non trivial solution is 4

Step-by-step explanation:

For a non trivial solution, the value of |A| = 0

Given

system of linear equations

x+3y+((lambda)+2)z=0

2x+4y+8z=0

3x+5y+10z=0

|A| = 0

$\left[\begin{array}{ccc}1&3λ + 2\\2&4&8\\3&5&10\end{array}\right]$         =  0

⇒1( 4*10 - 5*8) - 3(2*10 - 3*8) + (lambda +2 )(2*5 - 3*4) = 0

⇒(40 - 40) - 3(20 - 24) +  (lambda +2 )(10 - 12) = 0

⇒12 - 2 (lambda +2 ) = 0

⇒2 (lambda +2 )  = 12

⇒ (lambda +2 ) = 6

⇒ lambda = 6 - 2

⇒  lambda = 4

∴The value of lambda for which the system of solutions will have a non trivial solution is 4.

The project code is #SPJ2.