JEE Main 2020MathematicsMatricesEasyMCQ

JEE Main 2020 — Matrices Question with Solution

JEE Main 2020 (02 Sep Shift 2)

Question

Let A=X=x,y,zT:PX=0 and x2+y2+z2=1 where P=121-23-419-1 then the set A

Choose an option

Show full solutionCorrect option: D
Correct answer
DContains exactly two elements

Step-by-step explanation

∵  P=0

∴ System of equations 

x+2 y+z=0 

2x-3y+4z=0 

x+9y-z=0 has infinitely many solutions.

Let z=k∈R then x=-11k7, y=2k7, z=k 

Also x2+y2+z2=1 

∴k=±7174 

∴ Two solutions are only possible.

Hence, set A contains exactly two elements.

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About this question

This is a previous-year question from JEE Main 2020, 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.