Questions
Let A and B be real matrices such that A is symmetric matrix and B is skew-symmetric matrix. Then the system of linear equations , where X is a column matrix of unknown variables and O is a null matrix, has
detailed solution
Correct option is B
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 solutionsSimilar Questions
If the system of equations,
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