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LetA=a1a2 and B=b1b2 be two 2×1matrices with real entries such that A=XB, where X=131−11k, and k∈R. If a12+a22=23b12+b22and  k2+1b22≠−2b1b2, then the value of k is _____

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answer is 1.

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Detailed Solution

A=XB∴a1a2=131-11kb1b2=13b1-b2b1+kb2⇒a1=13b1-b2 and a2=13b1+kb2              Given that a12+a22=23b12+b2213b1−b22+13b1+kb22=23b12+b221+k2b22+2b12+2k−1b1b2=2b12+2b22k2−1b22+2k−1b1b2=0k−1k+1b22+2b1b2=0k=1
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LetA=a1a2 and B=b1b2 be two 2×1matrices with real entries such that A=XB, where X=131−11k, and k∈R. If a12+a22=23b12+b22and  k2+1b22≠−2b1b2, then the value of k is _____