Algebra 1 Common Core Student Edition, Grade 8-9

Concept Byte

Use W ith Lesson 6-3

i

Matrices and

So l v i n g Sy st e m s

A matrix is a rectangular a rran g em en t of n u m b ers in rows a n d colum ns. I h e plural of

matrix is matrices. You will learn m ore ab o u t m atrix operations, including adding an d

subtracting matrices, in Chapter 12.

You can use a special type of m atrix, called an augm ented m atrix, to solve a system of

linear equations. An augm ented m atrix is form ed using th e coefficients an d constants

in the equations in a system. The equations m u st be w ritten in stan d ard form.

Augmented Matrix

7 6 10

_4 5 to 1

System of Equations

7x + 6y = 10

4x + 5y = -5

Recall th e operations you p erfo rm ed w h en you solved system s using elim ination. You

can perform sim ilar operations on th e rows of a n a u g m en te d matrix.

You can perform any of th e following row operations on an au g m en ted m atrix to

p roduce an equivalent au g m en ted m atrix.

Common Core State Standards

Extends A-REI.C.6 Solve systems of linear

equations exactly and approximately (e.g., with

graphs), focusing on pairs of linear equations in

tw o variables.

MP 6

Interchange two rows.

Multiply a row by any constant except 0.

Add a m ultiple of one row to a n o th er row.

To solve a system using an a u g m en ted matrix, choose row operations th a t will

transform the au g m en ted m atrix into a m atrix w ith l 's along th e m ain diagonal (top

left to lower right) a n d 0’s above an d below th e m ain diagonal, as show n below.

76 10 4 5 - 5

_4 5 —5_ _7 6 10_

~7 6 10 "7^610 ~7^610

_4 5 —5 _ _2(4) 2(5) 2 (—5)_ _8^10 —1 0 _

~7 6 10~ 7 + 2(4) 6 + 2(5) 10 + 2 (--5)~^15 160

_4 5—5_^45 -5 _^5 —5 _

1 's along the

main diagonal

0 ’s elsewhere

Co n st a n t s

on t he right

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