If the system of linear equations x + k y + 3 z = 0 3 x + k y - 2 z = 0 2 x + 4 y - 3 z = 0 has a non-zero solution x ,   y ,   z , then x z y 2 is equal to:

Question

If the system of linear equations x + k y + 3 z = 0 3 x + k y - 2 z = 0 2 x + 4 y - 3 z = 0 has a non-zero solution x , &#160; y , &#160; z , then x z y 2 is equal to:

Aicharya · Accepted Answer

1 k 3 3 k - 2 2 4 - 3 = 0 &#8658; - 3 k + 8 - 3 - 3 k - 12 + 2 - 5 k = 0 &#8658; - 4 k + 44 = 0 &#8658; k = 11 &#8658; x + 11 y + 3 z = 0 &#160; &#160; &#160; . . . 1 &#8658; 3 x + 11 y - 2 z = 0 &#160; &#160; &#160; . . . 2 &#8658; 2 x + 4 y - 3 z = 0 &#160; &#160; &#160; . . . 3 On solving equations 1 &#160; &#38; &#160; 2 , we get 2 x - 5 z = 0 &#8658; x = 5 z 2 Put it in equation 3 , we get 2 z + 4 y = 0 &#8658; z = - 2 y &#8756; x z y 2 = - 2 y &#215; - 5 y y 2 = 10

If the system of linear equations x + k y + 3 z = 0 3 x + k y - 2 z = 0 2 x + 4 y - 3 z = 0 has a non-zero…

Solution