# Chapter 5 - Matrices 1 Flashcards

## Matrix Properties, Arithmetic, Transformations, and Equations... what's it going to be? The red pill? Or the blue pill?

Describe a matrix of an order n x m.

How do determine the order of a matrix?

A matrix with n rows and m columns has order n x m.

What is possible on two matrices that have the same order?

If two matrices have the same order then they can be added or subtracted by adding or subtracting their corresponding elements.

What is the rule regarding matrices being multiplied by constants?

To multiply a matrix by a constant, multiply each of its elements by that constant.

What is the zero matrix?

The zero matrix is a matrix of any order with all elements equal to zero.

If two matrices can be multiplied, what are those matrices known to be able to do?

If two matrices can be multiplied, then it is said that they are conformable for multiplication.

What is the order of the product of matrices n x m, and m x p?

The product of matrices n x m and m x p has order n x p.

What is the rule for squaring matrices?

It is only possible to square a matrix if it is a square matrix, meaning the matrix has the same number of orders as rows.

How do you transpose a matrix?

You transpose a matrix by swapping the rows and columns.

How do you find the image of a vector?

In order to find the image of a vector (x,y) under a transformation T = (a b, c d) (2x2), we premultiply the vector by the matrix. (T x vector)

How do you represent a reflection in the line y = x?

The matrix

( 0 1 )

( 1 0 )

represents a reflection in the line y = -x.

How do you represent a reflection in the line y = -x?

The matrix

( 0 -1 )

( -1 0 )

represents a reflection in the line y = -x.

What is the identity matrix?

The matrix, I =

( 1 0 )

( 0 1 )

is the identity matrix, which works on all 2x2 matrices. Multiplying this transformation has no effect on the original vector.

What matrix represents a stretch of scale factor k parallel to the x-axis?

The matrix

( k 0 )

( 0 1 )

represents a stretch of scale factor k parallel to the x-axis.

What matrix represents a stretch of scale factor k parallel to the y-axis?

The matrix

(1 0)

(0 k)

represents a stretch of scale factor k parallel to the y-axis.