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Question

Consider matrix A=[k2kk2kk2]and vector x=[x1x2]. The number of distinct real values of k for which the equation Ax=0 has infinitely many solutions is ______ .
  1. 2

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Solution

The correct option is A 2
A=[k2kk2kk2] and given system is AX = 0
We know that homogeneous system have infinite solution if |A|=0
k32k(k2k)=0
k32k3+2k2=0
k2(2k)=0
k=0,0,2
Hence k have two distinct values.

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