JEE Advanced 2016 Paper 1 Mathematics Q8

Mathematics

Problem

Let P=[3−1−220α3−50]P=\begin{bmatrix}3&-1&-2\\2&0&\alpha\\3&-5&0\end{bmatrix}, where α∈R\alpha\in\mathbb R. Suppose Q=[qij]Q=[q_{ij}] is a matrix such that PQ=kIPQ=kI, where k∈Rk\in\mathbb R, k≠0k\ne0 and II is the identity matrix of order 3. If q23=−k8q_{23}=-\frac{k}{8} and det⁡(Q)=k22\det(Q)=\frac{k^2}{2}, then

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