Question

Find value of K such that system of equations are,(3k-8)x+3y+3z=0 ,3x+(3k-8)y+3z=0 , 3x+3y+(3k-8)z=0 has non- trivial solution​

Answer 1

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Answer 2

Given : system of equations of (3k-8)x+3y+3z=0 ,3x+(3k-8)y+3z=0 , 3x+3y+(3k-8)z=0  has non trivial solution

To find : Value of k

Solution:

(3k-8)x+3y+3z=0

3x+(3k-8)y+3z=0

3x+3y+(3k-8)z=0

No trivial solution if

$\left[\begin{array}{ccc}3k-8&3&3\\3&3k-8&3\\3&3&3k-8\end{array}\right] =0$

k = 2/3  , 11/3

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