Every 3x3 skew symmetric matrix is singular. Because this is a skew symmetric matrix, det(A)=det(A^T)=det(−A)=(−1)^n det(A), and when n is odd det(A)=−det(A), so 2det(A)=0 and therefore det(A)=0. As such, the answer is "False" because it is only singular when n is odd.

engausidarb

engausidarb

Answered question

2022-09-07

Every 3 × 3 skew symmetric matrix is singular. Because this is a skew symmetric matrix, det ( A ) = det ( A T ) = det ( A ) = ( 1 ) n det ( A ), and when n is odd det ( A ) = det ( A ), so 2 det ( A ) = 0 and therefore det ( A ) = 0. As such, the answer is "False" because it is only singular when n is odd.

Answer & Explanation

Ashlynn Cox

Ashlynn Cox

Beginner2022-09-08Added 12 answers

By your reasoning it's true since we're only considering n = 3.

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