JEE-Advanced 2015 (9/40)

Algebra Level 5

Let \(X\) and \(Y\) be two arbitrary, \(3 \times 3\), non-zero, skew-symmetric matrices and \(Z\) be an arbitrary, \(3 \times 3\), non-zero , symmetric matrix. Then which of the following matrices is (are) skew-symmetric ? \[\begin{array}{} (1) \, Y^3Z^4-Z^4Y^3 \quad \quad \quad \quad & (2) \, X^{44}+Y^{44} \\ (3) \, X^4Z^3-Z^3X^4 & (4) \, X^{23}+Y^{23} \end{array}\]
Note :

  • Submit your answer as the increasing order of the serial numbers of all the correct options.

  • For eg, if your answer is \((1),(2)\), then submit 12 as the correct answer, if your answer is \((2),(3),(4)\), then submit 234 as the correct answer.

×

Problem Loading...

Note Loading...

Set Loading...