JEE PYQ: Matrices And Determinants Question 5
Question 5 - 2021 (16 Mar Shift 2)
Let $A = \begin{bmatrix} a_1 \ a_2 \end{bmatrix}$ and $B = \begin{bmatrix} b_1 \ b_2 \end{bmatrix}$ be two $2 \times 1$ matrices with real entries such that $A = XB$, where $X = \dfrac{1}{\sqrt{3}}\begin{bmatrix} 1 & -1 \ 1 & k \end{bmatrix}$, and $k \in \mathbb{R}$.
If $a_1^2 + a_2^2 = \dfrac{2}{3}(b_1^2 + b_2^2)$ and $(k^2 + 1)b_2^2 \neq -2b_1 b_2$, then the value of $k$ is ______.
BETA
