Consider matrix A=[k2kk2−kk2]and vector x=[x1x2]. The number of distinct real values of k for which the equation Ax=0 has infinitely many solutions is ______ .
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The correct option is A 2 A=[k2kk2−kk2] and given system is AX = 0
We know that homogeneous system have infinite solution if |A|=0 k3−2k(k2−k)=0 ⇒k3−2k3+2k2=0 ⇒k2(2−k)=0 ⇒k=0,0,2
Hence k have two distinct values.