Question

Properties Of Determinants ?

Answer 1

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Properties of determinants

Interchange two rows or cols changes the sign: -> -1 * det(A) ...transpose -> det (A) unchanged. ...multiply row * k -> k * det(A) ...multiply matrix * k -> k^2 * det(A) ...det (A B) -> det(A) * det(B) ...proportional rows or columns -> det() == 0. ...Add multiple of one row to another -> det unchanged. ...Geometric interpretation.

$\color{pink} \infty \infty \infty \infty \infty \infty \infty \infty \infty \infty \infty \infty$
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Answer 2

1.The value of determinant remains unchanged if rows and columns are interchanged. 2. if any two rows or columns are interchanged then the sign of the determinant change s. 3.if any rows or columns are identical ,the it's value is zero . 4. if each element is multiplied by a constant k ,then it's value gets multiplied by k.5.if some or all the elements of a row or columns are expressed as the sum of two or more terms ,the the determinant can be expressed as the sum of two or more determinants. 6 . if to each element of any row or columns of a determinant ,a multiple of another row or columns is added ,the value of the determinant remains the same..