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This module explains using and solving matrices on a calculator.

Many modern graphing calculators have all the basic matrix operations built into them. The following is a brief overview of how to work with matrices on a TI-83, TI-83 Plus, TI-84, or TI-84 Plus.

The calculator has room to store up to ten matrices at once. It refers to these matrices as [A], [B], and so on, through [J]. Note that these are not the same as the 26 lettered memories used for numbers.

The following steps will walk you through the process of entering and manipulating matrices.

  • Hit the MATRX button. On a TI-83, this is a standalone button; on a TI-83 Plus, you first hit 2nd and then MATRIX (above the x –1 button). The resulting display is a list of all the available matrices. (You have to scroll down if you want to see the ones below [G] .)
  • Hit the right arrow key ► twice, to move the focus from NAMES to EDIT . This signals that you want to create, or change, a matrix.
  • Hit the number 1 to indicate that you want to edit the first matrix, [A] .
  • Hit 4 ENTER 3 ENTER to indicate that you want to create a 4x3 matrix. (4 rows, 3 columns.)
  • Hit 1 ENTER 2 ENTER 3 ENTER 4 ENTER 5 ENTER 6 ENTER7 ENTER 8 ENTER 9 ENTER 10 ENTER 11 ENTER 12 ENTER This fills in the matrix with those numbers (you can watch it fill as you go). If you make a mistake, you can use the arrow keys to move around in the matrix until the screen looks like the picture below.
  • Hit 2nd Quit to return to the main screen.
  • Return to the main matrix menu, as before. However, this time, do not hit the right arrow to go to the EDIT menu. Instead, from the NAMES menu, hit the number 1 . This puts [A] on the main screen. Then hit ENTER to display matrix [A] .
  • Go through the process (steps 1-7) again, with a few changes. This time, define matrix [B] instead of matrix [A] . (This will change step 3: once you are in the EDIT menu, you will hit a 2 instead of a 1.) Define [B] as a 3x2 matrix in step 4. Then, in step 5, enter the following numbers:
    10 40 20 50 30 60 size 12{ left [ matrix { "10" {} # "40" {} ##"20" {} # "50" {} ## "30" {} # "60"{}} right ]} {}
    When you are done, and have returned to the main screen and punched 2 in the NAMES menu (step 7), your main screen should look like this:
  • Now, type the following keys, watching the calculator as you do so. TI-83 Plus users should always remember to hit 2nd MATRIX instead of just MATRX. MATRX 1 + MATRX 2
    This instructs the computer to add the two matrices. Now hit ENTER
    Hey, what happened? You asked the computer to add two matrices. But these matrices have different dimensions . Remember that you can only add two matrices if they have the same dimensions—that is, the same number of rows as columns. So you got an “Error: Dimension Mismatch.” Hit ENTER to get out of this error and return to the main screen.
  • Now try the same sequence without the + key: MATRX 1 MATRX 2 ENTER
    This instructs the calculator to multiply the two matrices. This is a legal multiplication—in fact, you may recognize it as the multiplication that we did earlier. The calculator displays the result that we found by hand: 1 2 3 4 5 6 7 8 9 10 11 12 size 12{ left [ matrix { 1 {} # 2 {} # 3 {} ##4 {} # 5 {} # 6 {} ## 7 {} # 8 {} # 9 {} ##"10" {} # "11" {} # "12"{} } right ]} {} 10 40 20 50 30 60 size 12{ left [ matrix { "10" {} # "40" {} ##"20" {} # "50" {} ## "30" {} # "60"{}} right ]} {} = 140 320 320 770 500 1220 680 1670 size 12{ left [ matrix { "140" {} # "320" {} ##"320" {} # "770" {} ## "500" {} # "1220" {} ##"680" {} # "1670"{} } right ]} {}
  • Enter a third matrix, matrix [C]= 3 4 5 6 size 12{ left [ matrix { 3 {} # 4 {} ##5 {} # 6{} } right ]} {} . When you confirm that it is entered correctly, the screen should look like this:
    Now type MATRX 3 x-1 ENTER
    This takes the inverse of matrix [C]. Note that the answer matches the inverse matrix that we found before.
  • Type MATRX 3 x-1 MATRX 3 ENTER
    This instructs the calculator to multiply matrix [C]-1 times matrix [C]. The answer, of course, is the 2×2 identity matrix [I].

Questions & Answers

Is there any normative that regulates the use of silver nanoparticles?
Damian Reply
what king of growth are you checking .?
What fields keep nano created devices from performing or assimulating ? Magnetic fields ? Are do they assimilate ?
Stoney Reply
why we need to study biomolecules, molecular biology in nanotechnology?
Adin Reply
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
what school?
biomolecules are e building blocks of every organics and inorganic materials.
anyone know any internet site where one can find nanotechnology papers?
Damian Reply
sciencedirect big data base
Introduction about quantum dots in nanotechnology
Praveena Reply
what does nano mean?
Anassong Reply
nano basically means 10^(-9). nanometer is a unit to measure length.
do you think it's worthwhile in the long term to study the effects and possibilities of nanotechnology on viral treatment?
Damian Reply
absolutely yes
how to know photocatalytic properties of tio2 nanoparticles...what to do now
Akash Reply
it is a goid question and i want to know the answer as well
characteristics of micro business
for teaching engĺish at school how nano technology help us
Do somebody tell me a best nano engineering book for beginners?
s. Reply
there is no specific books for beginners but there is book called principle of nanotechnology
what is fullerene does it is used to make bukky balls
Devang Reply
are you nano engineer ?
fullerene is a bucky ball aka Carbon 60 molecule. It was name by the architect Fuller. He design the geodesic dome. it resembles a soccer ball.
what is the actual application of fullerenes nowadays?
That is a great question Damian. best way to answer that question is to Google it. there are hundreds of applications for buck minister fullerenes, from medical to aerospace. you can also find plenty of research papers that will give you great detail on the potential applications of fullerenes.
what is the Synthesis, properties,and applications of carbon nano chemistry
Abhijith Reply
Mostly, they use nano carbon for electronics and for materials to be strengthened.
is Bucky paper clear?
carbon nanotubes has various application in fuel cells membrane, current research on cancer drug,and in electronics MEMS and NEMS etc
so some one know about replacing silicon atom with phosphorous in semiconductors device?
s. Reply
Yeah, it is a pain to say the least. You basically have to heat the substarte up to around 1000 degrees celcius then pass phosphene gas over top of it, which is explosive and toxic by the way, under very low pressure.
Do you know which machine is used to that process?
how to fabricate graphene ink ?
for screen printed electrodes ?
What is lattice structure?
s. Reply
of graphene you mean?
or in general
in general
Graphene has a hexagonal structure
On having this app for quite a bit time, Haven't realised there's a chat room in it.
what is biological synthesis of nanoparticles
Sanket Reply
how did you get the value of 2000N.What calculations are needed to arrive at it
Smarajit Reply
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Source:  OpenStax, Advanced algebra ii: conceptual explanations. OpenStax CNX. May 04, 2010 Download for free at http://cnx.org/content/col10624/1.15
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