Explain the properties of determinants in a short way.
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1. Property of Reflection:If in a determinant, even when rows are interchanged with columns, the value of the determinant remains unaltered.
2. All Zero Property:If all the elements of any particular row or any particular column are zero then the value of the determinant is also zero.
3. Repetition Property:If there are two identical rows or columns then the value of the determinant is zero.
4. Switching Property:If any two rows or columns are interchanged then the value of the determinant changes its sign
5. Property of multiplication by a Scalar:If all the elements of a row or a column in a determinant are multiplied by a constant non-zero value then the value of the determinant also becomes a multiple of that constant
6. Property of Sum:If =∣∣ ∣∣a+xbcd+yefg+zhi∣∣ ∣∣.Then the value of determinant becomes equal to the sum of the determinants obtained by splitting
7. Property of In variance: If any row or column of a determinant is expressed as the sum of multiples of any other row or column then the value of the determinant remains unchanged.
8. Triangle Property:If, in a determinant all the elements above or below the diagonal consists of zero, only then the value of the determinant will be equal to the product of the diagonal element.
2. All Zero Property:If all the elements of any particular row or any particular column are zero then the value of the determinant is also zero.
3. Repetition Property:If there are two identical rows or columns then the value of the determinant is zero.
4. Switching Property:If any two rows or columns are interchanged then the value of the determinant changes its sign
5. Property of multiplication by a Scalar:If all the elements of a row or a column in a determinant are multiplied by a constant non-zero value then the value of the determinant also becomes a multiple of that constant
6. Property of Sum:If =∣∣ ∣∣a+xbcd+yefg+zhi∣∣ ∣∣.Then the value of determinant becomes equal to the sum of the determinants obtained by splitting
7. Property of In variance: If any row or column of a determinant is expressed as the sum of multiples of any other row or column then the value of the determinant remains unchanged.
8. Triangle Property:If, in a determinant all the elements above or below the diagonal consists of zero, only then the value of the determinant will be equal to the product of the diagonal element.
sasipriyankaj:
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