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GATE EC 2018 Set 1 — Question 32

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NAT+1 / -0MediumSystems of Linear EquationsLinear AlgebraEngineering MathematicsDeterminants

Engineering Mathematics → Linear Algebra → Determinants

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Question

Consider matrix A=[k2kk2−kk2]\mathbf{A} = \begin{bmatrix} k & 2k \\ k^2-k & k^2 \end{bmatrix} and vector x=[x1x2]\mathbf{x} = \begin{bmatrix} x_1 \\ x_2 \end{bmatrix}. The number of distinct real values of kk for which the equation Ax=0\mathbf{Ax} = \mathbf{0} has infinitely many solutions is _______.
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