Question

Which statements are true (Note: ∆ is the determinant): 1. Determinant functions, A={∆₄|∆₄:⁴r⁴ r is a vector space

Answer 1

The given statement is not true. The determinant of a matrix is not a vector space.

Step-by-step explanation:

The given statement is not true. The determinant of a matrix is not a vector space. The determinant is a scalar value that represents the size of the matrix and provides information about its invertibility.

In linear algebra, a vector space is a set of vectors with specific properties that satisfy certain axioms. The determinant does not fulfill these requirements and therefore cannot be considered a vector space.

For example, if we have a 2x2 matrix A:

A = [[a, b], [c, d]]

The determinant of A, denoted as ∆, is calculated as:

∆ = ad - bc

This is a scalar value, not a vector space.