Assertion: matrix's determinant | /r/HasProperty | equal
Facets:
value: to zero
type: OTHER
value: namely
type: DEGREE
value: to one
type: OTHER
value: to the product of determinants
type: OTHER
value: in a 2x2 matrix
type: OTHER
Source sentences:
text: In a 2x2 matrix, the determinant is equal to:
text: One of them is multiplicativity, namely that the determinant of a product of matrices is equal to the product of determinants.
text: When the determinant is equal to one, the linear mapping defined by the matrix is equi-areal and orientation-preserving.
text: The determinant of A, det ( A ) {\displaystyle \det(\mathbf {A} )} , is equal to the triple product of x 0 {\displaystyle \mathbf {x_{0}} } , x 1 {\displaystyle \mathbf {x_{1}} } , and x 2 {\displaystyle \mathbf {x_{2}} } —the volume of the parallelepiped formed by the rows or columns:
text: If all the determinants of the submatrices of order 3 were equal to zero, we would have to continue with the submatrices of order 2, until we found a determinant that was different from 0 and in that case, the range of the matrix would be 2.