If, we have any given matrix A then determinant of matrix A is equal to determinant of its transpose. We can prove this by taking variable
Archives for March 2012
What is the determinant of a matrix if all the elements in a row or column are zero?
If in a given matrix, we have all zero elements in a particular row or column then determinant of such a matrix is equal to zero.
Determinant of a Matrix having one row (column) multiple of another row (column) is equal to 0
If, we have any matrix in which one of the row (or column) is multiple of another row (or column) then determinant of such a matrix is equal to zero. We can prove this property by taking example of such a matrix and finding its determinant. It is one of the property of determinants. Therefore, if you see any matrix of the form in which one row (or column) is multiple of another row (0r column) then you can directly right value of its determinant equal to zero.
Let 3x 3 matrix
{One row is multiple of another row in matrix A}
Therefore, we can see that value of determinant of such a matrix is equal to zero. Similarly, we can prove that determinant of matrix
is equal to zero ( In this matrix we have one column multiple of another column).
Determinant of Skew-Symmetric Matrix is equal to Zero if its order is odd
It is one of the property of skew symmetric matrix. If, we have any skew-symmetric matrix with odd order then we can directly write its determinant equal to zero. We can verify this property using an example of skew-symmetric 3×3 matrix. We can find its determinant using co-factors and can verify that its determinant is equal to zero.
Determinant of a Matrix with two Identical rows or columns is equal to 0
It is one of the property of determinants. If, we have any matrix with two identical rows or columns then its determinant is equal to zero. We can verify this property by taking an example of matrix A such that its two rows or columns are identical.
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