Solving Systems Using Matrices

Section 7.2 & 7.3

Row x Column

Matrix

ROW

COLUMN

ax + by = cdx + ey = f

Matrix Equation

A BX

A∙X = B A-1 (A∙X) = A-1 (B)

X = A-1B

Solving Matrix Equations

2nd, x-1

→ EDITEnter in matrix A & B2nd, x-1

Select Matrix [A]Press x-1

2nd, x-1

Select Matrix [B]ENTER

Ex) Solve using a matrix equation

2x + y = 10x – 2y = -5

A matrix with only leading 1’s and 0’s everywhere else

Reduced Row Echelen Form

Solving using “ rref ”ax + by = cdx + ey = f

1. 2nd, x-1 → MATH

2. rref([A])

x = ry = s

Ex. Solve the system below by putting it into reduced row echelon form:

-2 2 -4 -3

-2R1 + R2

R1 + R3

Switch R2 and R3

0 -3 3 -12 -3R2 + R3

- ½ R3

1. y = -2x + 4 2. 5x + 2y = 8 y = -2x - 1 x – y = 10

3. 2x + y = 2 4. y = -2x – 4 -2x + 2y = 10 5x + 3y = -6

Solve using the given method

{ {

{ {

Substitution Matrices

Elimination Graphing