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QJEEM21Mab52a: JEE Main 2021 Mathematics - Class 12 JEEM21Mab52a Solution: Let M be any 3 3 matrix with entries from the set {0, 1, 2}.…

Let M be any 3 ×\times 3 matrix with entries from the set {0, 1, 2}. The maximum number of such matrices, for which the sum of diagonal elements of MTM is seven, is ________.

Step-by-Step Verified Solution

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a2+b2+c2+d2+e2+f2+g2+h2+i2=7{a^2} + {b^2} + {c^2} + {d^2} + {e^2} + {f^2} + {g^2} + {h^2} + {i^2} = 7

Case I : Seven (1's) and two (0's)

Number of such matrices = 9C2=36{}^9{C_2} = 36

Case II : One (2) and three (1's) and five (0's)

Number of such matrices = 9!5!3!=504{{9!} \over {5!3!}} = 504

∴\therefore Total = 540

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