Let A and B be 3 × 3 real matrices such that A is a symmetric matrix and B is a skew-symmetric matrix. Then the system of linear equations A 2 B 2 - B 2 A 2 X = O , where X is a 3 × 1 column matrix of unknown variables and O is a

Question

Let A and B be 3 &#215; 3 real matrices such that A is a symmetric matrix and B is a skew-symmetric matrix. Then the system of linear equations A 2 B 2 - B 2 A 2 X = O , where X is a 3 &#215; 1 column matrix of unknown variables and O is a 3 &#215; 1 null matrix, has

Quantrex Academy · Accepted Answer

Correct answer: B. infinitely many solutions

Let A T = A and B T = - B C = A 2 B 2 - B 2 A 2 C T = A 2 &#160; B 2 T - B 2 &#160; A 2 T = B 2 T A 2 T - A 2 T B 2 T = B 2 &#160; A 2 - A 2 &#160; B 2 C T = - C C is skew symmetric. So det C = 0 so system have infinite solutions.

Let A and B be 3 × 3 real matrices such that A is a symmetric matrix and B is a skew-symmetric matrix. Then the system of linear equations A 2 B 2 - B 2 A 2 X = O , where X is a 3 × 1 column matrix of unknown variables and O is a 3 × 1 null matrix, has

Options

Correct answer

Step-by-step solution

More from Determinants

Let A and B be 3 &#215; 3 real matrices such that A is a symmetric matrix and B is a skew-symmetric matrix. Then the system of linear equations A 2 B 2 - B 2 A 2 X = O , where X is a 3 &#215; 1 column matrix of unknown variables and O is a 3 &#215; 1 null matrix, has

Options

Correct answer

Step-by-step solution

More from Determinants

Let A and B be 3 × 3 real matrices such that A is a symmetric matrix and B is a skew-symmetric matrix. Then the system of linear equations A 2 B 2 - B 2 A 2 X = O , where X is a 3 × 1 column matrix of unknown variables and O is a 3 × 1 null matrix, has