JEE Main 2021MathematicsMatricesHardNumerical

JEE Main 2021 — Matrices Question with Solution

JEE Main 2021 (24 Feb Shift 1)

Question

Let P=3-1-220α3-50, where α∈R. Suppose Q=qij is a matrix satisfying PQ=kI3 for
some non-zero k∈R. If q23=-k8 and Q=k22, then α2+k2 is equal to_________.

Enter your answer

Show full solutionCorrect answer: 17
Correct answer
17

Step-by-step explanation

PQ=kI

P.Q=k3

⇒ P=2k≠0⇒P is an invertible matrix

∵ PQ=kI

∴ Q=kP-1I

∴ Q= adj.P2

∵ q23=-k8

∴ -3α+42=-k8⇒k=4

∴ P=2k⇒k=10+6α    …i

Put value of k in i.. we get α=-1

⇒α2+k2=17

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About this question

This is a previous-year question from JEE Main 2021, covering the Matrices chapter of Mathematics. PrepSharp catalogues every PYQ from JEE Main with a verified answer key and step-by-step solution prepared by IIT alumni — so you can search by chapter, topic or year and revise efficiently.