Let A and B be $$3$$×$$3$$ real matrices such that A is symmetric matrix and B is $$skew-symmetric$$ matrix. Then the system of linear equations $$A2B2$$−$$B2A2X=0$$, where X is a $$3$$×$$1$$ column matrix of unknown variables and O is a $$3$$×$$1$$ null matrix, has

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Let A and B be $$3$$×$$3$$  real matrices such that A is symmetric matrix and B is $$skew-symmetric$$ matrix. Then the system of linear equations  $$A2B2$$−$$B2A2X=0$$, where X is a  $$3$$×$$1$$ column matrix of unknown variables and O is a  $$3$$×$$1$$ null matrix, has

Infinity Learn · Accepted Answer

Given $$AT=A$$,        $$BT=-B$$         given system is homogenous system of equationsDeterminant of coefficient matrix  is $$A2B2$$−$$B2A2Consider$$ $$A2B2$$−$$B2A2T=A2B2)T$$−$$(B2A2T$$ $$=B2A2-A2B2$$ $$=-A2B2$$−$$B2A2Therefore$$, $$A2B2$$−$$B2A2$$ is a skew symmetric matrix of odd orderHence the determinant of the coefficient matrix is zero. Therefore, the system of equations have non trivial solutions, and it has infinitely many solutions

Let A and B be $3 \times 3$ real matrices such that A is symmetric matrix and B is skew-symmetric matrix. Then the system of linear equations $(A^{2} B^{2} - B^{2} A^{2}) X = 0$ , where X is a $3 \times 1$ column matrix of unknown variables and O is a $3 \times 1$ null matrix, has

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Let A and B be 3×3 real matrices such that A is symmetric matrix and B is skew-symmetric matrix. Then the system of linear equations A2B2−B2A2X=0, where X is a 3×1 column matrix of unknown variables and O is a 3×1 null matrix, has

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Ready to Test Your Skills?

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Let A and B be $3 \times 3$ real matrices such that A is symmetric matrix and B is skew-symmetric matrix. Then the system of linear equations $(A^{2} B^{2} - B^{2} A^{2}) X = 0$ , where X is a $3 \times 1$ column matrix of unknown variables and O is a $3 \times 1$ null matrix, has