JEE Main 2017MathematicsMatricesMediumMCQ

JEE Main 2017 — Matrices Question with Solution

JEE Main 2017 (09 Apr Online)

Question

For two 3×3 matrices A and B, let A+B=2B' and 3A+2B=I3, where B′ is the transpose of B and I3 is 3×3 identity matrix. Then :

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Show full solutionCorrect option: A
Correct answer
A10A+5B=3I3

Step-by-step explanation

Given A+B=2 B T

⇒ AT+BT=2B

⇒     B=AT+BT2

=A+BT+AT2=2BT

2A+AT=3BT

⇒     A=3BT-AT2

3A+2B=I3 ......i

⇒      33BT-AT2+2AT+BT2=I3

⇒    3BT+2BT2+2AT+BT2=I3

⇒      11BT-AT=2I3 .......ii

Equation i+ii

35B=7I3

⇒ B=I35

11 I35-A=2I3

⇒     11I35-2I3=A

⇒    A=I35

∵      5A=5B=I3

⇒       10A+5B=3I3

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About this question

This is a previous-year question from JEE Main 2017, 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.