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

Option 1 -

A unique solution

Option 2 -

Exactly two solutions

Option 3 -

Infinitely many solutions

Option 4 -

No solution

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Answered by

alok kumar singh | Contributor-Level 10

a month ago

Correct Option - 3

Detailed Solution:

$A^{T} = A a n d B^{T} = - B$

$C = A^{2} B^{2} - B^{2} A^{2}$

$C^{T} = {(A^{2} B^{2})}^{T} - {(B^{2} A^{2})}^{T} = B^{2} A^{2} - A^{2} B^{2}$

C^T = -C. Hence C is skew symmetric metrix

$∴$ det (C) = 0

Hence system have infinite solution

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alok kumar singh

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Given x + 2y – 3z = a

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Kindly go through the solution

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