If the system of linear equations x + y + 3 z = 0 x + 3 y + k 2 z = 0 3 x + y + 3 z = 0 has a non-zero solution ( x ,   y ,   z ) for some k ∈ R , then x + y z is equal to :

Question

If the system of linear equations x + y + 3 z = 0 x + 3 y + k 2 z = 0 3 x + y + 3 z = 0 has a non-zero solution ( x , &#160; y , &#160; z ) for some k &#8712; R , then x + y z is equal to :

Aicharya · Accepted Answer

So D = 0 &#8594; 1 1 3 1 3 k 2 3 1 3 = 0 &#160;&#160; &#8658; &#160;&#160; k 2 = 9 x + y + 3 &#160; z = 0 x + 3 &#160; y + 9 &#160; z = 0 3 &#160; x + y + 3 &#160; z = 0 ( 1 ) - ( 3 ) x = 0 &#8658; &#160;&#160; y + 3 z = 0 &#8658; y z = - 3 so , &#160; x + y z = - 3

If the system of linear equations x + y + 3 z = 0 x + 3 y + k 2 z = 0 3 x + y + 3 z = 0 has a non-zero…

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