What is calculated from a matrix by cross multiplying and applying subtraction?

The term that describes what is calculated from a matrix by cross multiplying and applying subtraction is the determinant. The determinant is a scalar value that provides important information about a matrix, including whether the matrix is invertible and the volume scaling factor of the linear transformation represented by the matrix.

To calculate the determinant of a 2x2 matrix, for example, you use the formula (ad - bc) where the matrix is represented as:

[

\begin{pmatrix}

a & b \

c & d \

\end{pmatrix}

]

This involves cross multiplying the elements across the diagonal (a * d) and subtracting the product of the off-diagonal elements (b * c).

For larger matrices, the determination process involves more complex operations, including expanding along a row or a column, which can also include cross multiplying and applying subtraction. This reflects how determinants are formed in the context of linear transformations and adjacency in matrix theory.

The other terms, while related to matrices, do not encompass the same meaning or calculation method as the determinant. The co-factor is an auxiliary value used in the calculation of determinants, a submatrix refers to a smaller matrix derived from a larger matrix by deleting rows and columns, and the