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Let A=[{:(a(1)),(a(2)):}] and B= [{:(b(1...

Let `A=[{:(a_(1)),(a_(2)):}] and B= [{:(b_(1)),(b_(2)):}]` be two `2xx1` matricews with real entires such that `A=XB`, where `x=(1)/(sqrt(3))[{:(1,-1),(1,k):}], and k in R`. If `a_(1)^(2) +a_(2)^(2)=(2)/(3) (b_(1)^(2)+b_(2)^(2)) and (k^(2)+1)b_(2)^(2) ne-2b_(1) b_(2)` then the value of k is.....

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