Matrices review pre flashcard

A matrix is a rectangular array of numbers, symbols, or expressions, arranged in rows and columns.

Matrix multiplication involves multiplying rows of the first matrix by columns of the second matrix, resulting in a new matrix.

The number of columns in the first matrix must equal the number of rows in the second matrix.

For a matrix [[a, b], [c, d]], the determinant is calculated as ad - bc.

The determinant of a 3x3 matrix can be calculated using the rule of Sarrus or cofactor expansion.

If the determinant is zero, the matrix is singular, meaning it does not have an inverse.

An identity matrix is a square matrix with ones on the diagonal and zeros elsewhere.

The inverse of a matrix A is another matrix, denoted A^-1, such that AA^-1 = I, where I is the identity matrix.

Scalar multiplication involves multiplying each element of a matrix by a scalar (a constant number).

The transpose of a matrix is obtained by flipping it over its diagonal, switching the row and column indices.