MATRICES AND DETERMINANTS

What is a determinant?

It arises from eliminating unknowns in simultaneous equations.

How is a second-order determinant represented?

By enclosing two rows of elements in vertical bars.

What does the expansion of a determinant represent?

The relationship between the elements of the determinant.

What is a minor in the context of determinants?

A determinant obtained by deleting a specific row and column.

How is a cofactor calculated?

By multiplying the minor by (-1) raised to the sum of its row and column indices.

What happens when two rows of a determinant are interchanged?

The sign of the determinant changes.

What is the implication of identical rows in a determinant?

The value of the determinant is zero.

What effect does multiplying a row by a constant have on a determinant?

The determinant is multiplied by that constant.

What is the Rule of Sarrus used for?

To expand third-order determinants.

What is the condition for a determinant to remain unchanged?

Interchanging rows with columns does not alter its value.