Question

If the system of equation 2x + 5y + 8z = 0, x + 4y + 7z = 0, 6x + 9y – αz = 0 has a non trivial solution then what is the value of α?

(a) -12

(b) 0

(c) 12

(d) 2

This question was addressed to me in an online quiz.

This intriguing question comes from Application of Determinants topic in section Determinants of Mathematics – Class 12

Answer 1

Right choice is (c) 12

To explain I would say: Here, in L.H.S we have,

\(\begin{vmatrix}2 & 5 & 8 \\1 & 4 & 7 \\6 & 4 & \alpha \end {vmatrix}\)

So, for trivial roots the above value is = 0

=>\(\begin{vmatrix}2 & 5 & 8 \\1 & 4 & 7 \\6 & 4 & \alpha \end {vmatrix}\) = 0

Solving it further we get α = 12