JEE Main 2015 · 4 Apr · Shift 1 · Mathematics Q65

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The set of all values of λ for which the system of linear equations :
$2x_1-2x_2+x_3=\lambda x_1$
$2x_1-3x_2+2x_3=\lambda x_2$
$-x_1+2x_2=\lambda x_3$
has a non-trivial solution,

is an empty set.

is a singleton.

contains two elements.

contains more than two elements.

Answer and worked solution

Official answer: C

Non-trivial solutions need $\det(A-\lambda I)=0$ for $A=\begin{bmatrix}2&-2&1\\2&-3&2\\-1&2&0\end{bmatrix}$ :
$\lambda^3+\lambda^2-5\lambda+3=(\lambda-1)^2(\lambda+3)=0.$
So λ ∈ {1, −3}: two elements.

Topics:Systems of linear equations Determinants and properties

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JEE Main 2015 · 4 Apr · Shift 1, Mathematics question 65