# Chapter 4 terms

## 37 terms

### Matrix

is a rectangular array of numbers written within brackets.

### Matrix element

Each number in a matrix is a matrix element.

You perform matrix addition on matrices with equal dimensions by adding the corresponding elements, which are elements in the same position in each matrix.

### Zero matrix

The additive identity matrix for the set of all m X n matrices is the zero matrix O, or Om x n , whose elements are all zeros.

### Matrix subtraction

If two matrices, A and B, have the same dimensions, then A - B = A +

### matrix equation

A matrix equation is an equation in which the variable is a matrix.

### Equal matrices

Equal matrices are matrices with the same dimensions and equal corresponding elements.

### 5 properties chart pg 171

5 properties chart pg 171

### scalar

a variable quantity that cannot be resolved into components

### scalar product

a real number and a matrix is calculated by multiplying each element of the matrix by the scalar

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### matrix multiplication

Performed by multiplying the elements of each row of the first matrix by the elements of each column of the second matrix. Add the products.

### Dimensions of a Product

If matrix A is an m X n matrix and matrix B is an n X p matrix, then the
product matrix AB is a n / n X p matrix

### 4 properties of matrix multiplication chart pg 182

4 properties of matrix multiplication chart pg 182

### transformation

a function that changes the position or direction of the axes of a coordinate system

### image

a transformed figure

### preimage

The original figure in a transformation.

### translation

a transformation in which the origin of the coordinate system is moved to another position but the direction of each axis remains the same

### dilation

is a transformation that changes the size of a figure.

### reflection

A reflection, or flip, is a transformation that creates symmetry on the coordinate plane.

### rotation

A rotation is a transformation that turns a figure about a fixed point

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chart

### square matrix

a matrix with the same number of rows and columns

### multiplicative identity matrix

or an n X n square matrix, the multiplicative identity matrix is an n X n square matrix /, or In x n, with l's along the main diagonal and O's elsewhere.

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### coefficient matrix

a matrix whose entries are the coefficients of each variable in a system

### variable matrix

matrix containing the variables of the system

### constant matrix

The matrix of the constants in a linear system of equations.

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### augmented matrix

a matrix that is derived from a system of linear equations where each is written in standard form

### row operations

To solve a system of equations using an augmented matrix, you can use one or more of the following row operations: -Switch any tow rows. -Multiply a row by a constant. -Add one row to another. -Combine one or more of these steps.