Cool math fractal

math image

math image

pre-algebra help lessonsalgebra help lessonsprecalculus / calculus help lessonsmath anxiety survival guidegeometry math artmath and jigsaw puzzlesCoolmath booksother math stuff
math help lessonsmath practice problemsmath gamesmath dictionarygeometry trigonometry reference area
teacher's areaparent's areaCoolmath 4 kidsSpike's Game ZoneFinance FREAKTotally Stressed OutScience Monster
Coolmath Algebra
Matrices Lesson 5 - The Identity Matrix (page 2 of 3)
---- This algebra lesson explains what the identity is and how it works

math image
Now available: Coolmath Algebra books! Part 1, Part 2 and Part 3 covering the Algebra you need from Algebra 1 through Precalculus Algebra (Beginning Algebra through College Algebra)

other Coolmath Books: Coolmath Precalculus Review (the math you really need to survive Calculus 1) and Math Survival Guide (How to conquer math and deal with math anxiety)
line
Graphing Calculator Scientific Calculator << a new window will open for these
line

Why is he called the identity?

Remember the multiplicative identity for regular numbers?

What can you multiply 3 by so he stays a 3?

1!

3 times 1 = 3

AND

 1 times 3 = 3

It works both ways!

It's the same for our identity matrix!

A = [ row 1: 2 , -6 row 2: -5 , 8 ]

I = [ row 1: 1 , 0 row 2: 0 , 1 ]
 
A times I = A

AND

I times A = A

By the way, this guy is the 2 x 2 identity:

I = [ row 1: 1 , 0 row 2: 0 , 1 ]

So, what's the 3 x 3 identity?

I = [ row 1: 1 , 0 , 0 row 2: 0 , 1 , 0 row 3: 0 , 0 , 1 ]

The 4 x 4 identity?

I = [ row 1: 1 , 0 , 0 , 0 row 2: 0 , 1 , 0 , 0 row 3: 0 , 0 , 1 , 0 row 4: 0 , 0 , 0 , 1 ] ... Get the pattern? ... It's ones down the main diagonal and zeros everywhere else.

*All identity matrices are square.

Continued on the next page

 The printing and distribution and/or downloading of these lessons is strictly prohibited.
line
Graphing Calculator Scientific Calculator << a new window will open for these
line

.....:::::::::::::::  HELP SUPPORT COOLMATH  :::::::::::::::.....
:::::::  link to us   :::::::   advertise with us  :::::::  why we have ads  :::::::

Thanks for visiting Coolmath.com
© 1997-2010 Coolmath.com, Inc.