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Find the determinants of a rank one matrix and a skew-symmetric matrix: and [ 0 1 a= -1 0 -3 -

User Nate Bird
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Final answer:

The determinant of a rank one matrix is always zero unless it's a special case of a zero vector. The determinant of an odd-ordered skew-symmetric matrix is always zero, while an even-ordered skew-symmetric matrix can have a non-zero determinant.

Step-by-step explanation:

To find the determinants of a rank one matrix and a skew-symmetric matrix, it's important to understand the properties of these matrices.

A rank one matrix can be written in the form uvT, where u and v are column vectors. The determinant of such a matrix is always zero, unless one of the vectors is a zero vector, which is a special case.

A skew-symmetric matrix has the property that AT = -A. For a skew-symmetric matrix of odd order, the determinant is always zero. Meanwhile, a skew-symmetric matrix of even order can have a non-zero determinant, which can be found using standard determinant-finding techniques such as expansion by minors or using properties of determinants.

User Jack The Lesser
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