Let A = [(a1 a2)] and B = [(b1 b2)] be two 2 × 1 matrices with real entries such that A = XB,

Question

Let A = \(\left[ \begin{array}{c} a_1 \\ a_2 \end{array} \right]\) and B = \(\left[ \begin{array}{c} b_1 \\ b_2 \end{array} \right]\) be two 2 × 1 matrices with real entries such that A = XB, where \(X=\frac{1}{\sqrt{3}}\)\(\left[ \begin{array}{c} 1 & -1\\ 1 & k \end{array} \right],\) and k \(\in\) R. If

\(a^2_1+a^2_2=\frac{2}{3}(b^2_1+b^2_2)\) and \((k^2+1)b^2_2\neq -2b_1b_2,\) then the value of k is _______.

Answer 1

Answer is (1)