Question

In exercises 21–26, evaluate det() by a cofactor expansion along a row or column of your choice.

a) Row
b) Column
c) Both row and column
d) Neither row nor column

Answer 1

When evaluating the determinant (det) by a cofactor expansion, choosing either a column is a fundamental decision. (option b)

Step-by-step explanation:

In this case, the correct choice is column. The determinant is computed by expanding along a column using the cofactor expansion formula. Each term in the expansion involves a cofactor, which is determined by eliminating the row and column of the chosen element.

Let's consider a specific example to illustrate this. Suppose we have a 3x3 matrix:

A = [a b c; d e f; g h i]

To find det(A), we might choose the first column. The expansion would look like:

det(A) = a * cofactor(a) - d * cofactor(d) + g * cofactor(g)

This process is applied recursively for each element in the chosen column, providing a systematic approach to compute the determinant.

Choosing the correct row or column for cofactor expansion is essential for an accurate and efficient computation of the determinant, ensuring that the calculations align with the matrix structure and principles of linear algebra.(option b)