 # Matrices

## Vocabulary

### augmented matrix

matrix formed from two given matrices by writing the columns of the first matrix to the left of a vertical line and the columns of the second matrix to the right of the vertical line

### determinant

value calculated from the entries (or numbers) of a square matrix that provides information about the inverse of the matrix and the system of linear equations associated with the matrix

### dimensions

numbers of rows and columns of a matrix, written in the form $m\times n$, where $m$ is the number of rows and $n$ is the number of columns

### entry

each number in a matrix

### identity matrix

square matrix in which the numbers along the main diagonal, from the top left corner to the bottom right corner of the matrix, are ones and the other numbers are zeros

### inverse matrix

for a square matrix $A$, the matrix $A^{-1}$, such that $AA^{-1} = A^{-1}A = I$, where $I$ is the identity matrix

### matrix

rectangular array of numbers, enclosed by brackets

### matrix product

product of two or more matrices

### reduced row-echelon form

form of an augmented matrix in which the left side is the identity matrix

### row operations

operations that can be performed on a row of an augmented matrix to generate an equivalent matrix

### scalar

real number or a quantity that can be represented by a real number

### scalar product

product of a matrix and a real number called a scalar

### square matrix

matrix that has the same number of rows and columns