Give a direct proof of the following statement: “Every skew-symmetric matrix of odd order is singular”.

To prove that every skew-symmetric matrix of odd order is singular, we first need to establish what a skew-symmetric matrix is and what it means for a matrix to be singular.

A skew-symmetric matrix \( A \) is a square matrix where \( A^T = -A \), meaning the transpose of the matrix is equal to its negation. 

A matrix is singular if its determinant is zero. 

Now, let's _______ _______ _________ _____ _______ ________ ______ _________ ______ _________ _____.
____ ___ _____ ________ _________.
_____ _____ _____ ______ ________ __________.
____ __________ _____ ______ ___ __________ ________.
________ ___ ___ _________ __________ ____ ____ ______.
__________ _____ _______ ______ ______ _____ _________ ___ _______ ______ _______.
_____ ______ _________ __________ ___ ______ _______ __________ ____.
___ ___ _________ __________ ________ ___ ______ ___ ___ ______ ________ ___.
__________ ______ ________ __________ _____ __________ ________.
______ ______ ______ _____ _________ ________ _______ _____ ___ ________.
____ _______ _____ ______ ____ _____ _________ ________ _______ _______ ____ ________.
_______ _______ __________ ____ ______ ________ ________ _____ ____ ______ ________ ________.
____ ______ ____ _________ __________ __________ ___ ____ ______ ____ _________ _________.
____ __________ _______ ________ ____ _____ ____ ______.
______ ______ _____ ___ _________ _____ _______.
__________ ________ ______ ____ ___ ____ ____ ______ _______ ______ _________.
_____ ______ _____ ________ ____ ______ _________ __________ __________ _______.
_________ ____ _________ ___ ____ _______ ___.
____ _______ ____ ___ ____ ____ __________ ______ _________.
_____ ___ _________ __________ ______ ________.
___ _____ _____ _________ _______ _____.
_________ ________ ________ ___ _________.
_________ _________ _____ _________ _____ _______ _______ _____ ______.
_____ _____ ___ _____ ____ __________.
______ ______ __________ ___ _______ __________ ____ _________ __________.
______ _____ _________ ____ ___ ________ __________ ______ _______ _________ ____ __________.
__________ ______ ______ ___ ____ ______ __________ ________ __________.
_____ ___ ____ ____ ________ __________ ______ _______ ________ ____ __________ _____.
_________ ______ __________ ___ ___ _______.
___ ___ ___ ________ ___ ____ ___ ________ _________ _________.
________ _________ __________ __________ _______ ________ ________ __________ _____ _______ _____.
_________ _________ _____ _______ _________ _____ _________ _____.
___ ________ ____ _______ ______.
______ ____ __________ ________ ______ _____ ____ ______.
______ ________ __________ ____ _____ ______ ________ _______ ________ ____ __________.
____ _______ _________ _______ ________ ______ _________.
______ _____ ______ _________ ______.
______ ____ ______ _____ ____.
________ ____ _________ _____ _____ ________ _____ _________.
______ ___ _______ ___ _________ ____.
_______ ______ __________ __________ ________ ________ __________ __________ _____ _______.
Get Full Answer on WhatsApp