Let the system of linear equations 4 x + λ y + 2 z = 0 2 x - y + z = 0 μ x + 2 y + 3 z = 0 ,   λ ,   μ ∈ R has a non-trivial solution. Then which of the following is true?

Question

Let the system of linear equations 4 x + &#955; y + 2 z = 0 2 x - y + z = 0 &#956; x + 2 y + 3 z = 0 , &#160; &#955; , &#160; &#956; &#8712; R has a non-trivial solution. Then which of the following is true?

Aicharya · Accepted Answer

For non-trivial solution 4 &#955; 2 2 - 1 1 &#956; 2 3 = 0 &#8658; - 20 - 6 &#955; + &#955; &#956; + 8 + 2 &#956; = 0 &#8658; 2 &#956; - 6 &#955; + &#955; &#956; = 12 when &#956; = 6 , &#160; 12 - 6 &#955; + 6 &#955; = 12 which is satisfied by all &#955; When &#955; = 2 , &#160; 4 &#956; = 24 When &#955; = 3 , &#160; 5 &#956; = 30 When &#956; = - 6 , &#160; - 12 - 6 &#955; - 6 &#955; = 12

Let the system of linear equations 4 x + λ y + 2 z = 0 2 x - y + z = 0 μ x + 2 y + 3 z = 0 , &#160…

Solution

Let the system of linear equations 4 x + &#955; y + 2 z = 0 2 x - y + z = 0 &#956; x + 2 y + 3 z = 0 , &#160…

Solution

Let the system of linear equations 4 x + λ y + 2 z = 0 2 x - y + z = 0 μ x + 2 y + 3 z = 0 , &#160…