Question

Help me with this please

Answer 1

10

Explanation:

You want the determinant of the matrix ...

`\left[\begin{array}{cc}1&-2\\3&4\end{array}\right]`

Determinant

The determinant of a matrix is a sum of products. Each product is the element of a row or column multiplied by its cofactor.

For a 2×2 matrix, this becomes the difference between the product of diagonal terms and the product of off-diagonal terms:

(1·4) - (3·(-2))

= 4 +6

= 10

__

Additional comment

The cofactor of term a[i, j] is (-1)^(i+j)·det(M[i,j]), where M[i,j] is the minor matrix obtained by removing row i and column j from the original. As you can see, this definition of a determinant is recursive.

The above describes the determinant of a 2×2 matrix. The determinant of a 3×3 matrix resolves to a sum of 6 3-element products. For larger matrices, the computation burden can be reduced by taking advantage of rows or columns containing zeros.