Question

Compute the determinants using a cofactor expansion across the first row.

A) Gaussian elimination
B) Matrix inversion
C) Row reduction
D) Cramer's rule

Answer 1

There are multiple methods to compute determinants using a cofactor expansion across the first row, such as Gaussian elimination, matrix inversion, row reduction, and Cramer's rule.

Step-by-step explanation:

When computing determinants using a cofactor expansion across the first row, you can use several methods:

1. Gaussian elimination: This involves transforming the matrix into row-echelon form by performing row operations, and then obtaining the determinant from the product of the diagonal elements.
2. Matrix inversion: You can find the determinant by taking the inverse of the matrix and computing its determinant, which is equal to the reciprocal of the determinant of the original matrix.
3. Row reduction: Similar to Gaussian elimination, row reduction involves applying row operations to reduce the matrix to echelon form and finding the determinant from the product of the diagonal elements.
4. Cramer's rule: This method uses the determinant of the coefficient matrix to solve systems of linear equations. The determinant can be computed using cofactor expansion across the first row.