JEE Main 2021MathematicsMatricesMediumNumerical

JEE Main 2021 — Matrices Question with Solution

JEE Main 2021 (26 Feb Shift 2)

Question

If the matrix A=10002030-1 satisfies the equation A20+αA19+βA=100040001 for some real numbers α and β, then β-α is equal to ______.

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Show full solutionCorrect answer: 4
Correct answer
4

Step-by-step explanation

A=10002030-1

A2=100040001,A3=10008030-1

A4=1000160001

Hence, 

A20=10002200001,A19=1000219030-1

So A20+αA19+βA=1+α+β000220+α.219+2β03α+3β01-α-β=100040001

Therefore α+β=0 and 220+219α-2α=4

⇒α=41-2182218-1=-2

Hence β=2

So, β-α=4

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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.