Final answer:
To find the determinant of a matrix, one must perform a series of algebraic steps, including the use of cofactor expansion, row reduction, and the application of determinant properties.
Step-by-step explanation:
The student has asked to find the determinant of a matrix. The determinant is a scalar value that can be computed from the elements of a square matrix and is used in mathematical analysis and applied mathematics to determine the solvability of systems of linear equations, among other applications. The process of finding a determinant varies depending on the size of the matrix, but for a 2x2 matrix it involves multiplying the elements of the main diagonal and then subtracting the product of the off-diagonal elements.
To compute the determinant of a larger matrix, such as a 3x3 or higher, you typically perform operations that reduce the matrix to an upper or lower triangular form, or you may expand the determinant along a row or column using cofactors.
A common strategy when solving for determinants, especially in complex matrices, involves a variety of algebraic steps including cofactor expansion, row reduction, and using properties of determinants to simplify the process.