JEE Mains · Maths · STD 12 - 3 and 4 . metrices and determinant
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 \(M ^{ T } M\) is seven, is .............
- A \(512\)
- B \(556\)
- C \(560\)
- D \(540\)
Answer & Solution
Correct Answer
(D) \(540\)
Step-by-step Solution
Detailed explanation
\(\left[\begin{array}{lll}a & b & c \\ d & e & f \\ g & h & i\end{array}\right]\left[\begin{array}{lll}a & d & g \\ b & e & h \\ c & f & i\end{array}\right]\) \(a^{2}+b^{2}+c^{2}+d^{2}+e^{2}+f^{2}+g^{2}+h^{2}+i^{2}=7\) Case\(-I\) : Seven \((1's)\) and two \((0's)\)…
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