Skip to content
dronacharya.ai
← JEE Advanced 2017 · Paper 2
MathematicsSingle correct+3 / -1Question 41 of 54

JEE Advanced 2017 · Paper 2, Mathematics question 5

How many 3×33 \times 3 matrices MM with entries from {0,1,2}\{0, 1, 2\} are there, for which the sum of the diagonal entries of MTMM^TM is 5?

Choose one option
Answer and worked solution

Official answer: B

Trace. tr⁡(MTM)\operatorname{tr}(M^TM) is the sum of the squares of all nine entries. Each square is 0, 1 or 4.

Ways to make 5.

  • Five entries equal 1, the rest 0: (95)=126\binom95=126.
  • One entry equals 2, one equals 1, the rest 0: 9×8=729\times8=72.

Total. 126+72=198126+72=198.

(B)

Topics:CombinationsMatrix algebra
← Previous questionNext question →