Tip:
Highlight text to annotate it
X
This video is provided as supplementary material
for courses taught at Howard Community College, and in this video
I'm going to talk about row operations on the ti-83 and ti-84 calculator.
We're going to be dealing with matrices and we'll learn how to swap,
add and multiply rows within a matrix.
The first operation we're going to do
is swapping two rows in a matrix.
In the calculator here I've got a matrix displayed.
It's matrix A, and it's a 3 by 3 square matrix.
In this example I want to swap rows 2 and 3
of that matrix. So I go to the matrix menu.
I get there by pressing second
then I go down three buttons to the x-inverse button.
Right above that it says 'matrix'. Press that.
That gets us to the matrix menu. I want to go to the
math column. So Igo over to the right one,
and then what I want is at the bottom of that column. An easy way to get there is to
press the up button,
which takes me to the bottom, and I want to go up to
operations 'C',where it says
row swap. So I'll press Enter. I'm back at the main screen
and what I have to tell
the calculator to do a row swap is the name of the matrix
I'm going to be working with and then the numbers
fo the two rows that I want to swap. So I'll enter the name of the
matrix. That's matrix 'A'. I go back to the matrix menu.
In the names column I press '1' for matrix 'A'.
I have to put a comma after that.
Everything in this list will be separated by commas.
and then I want to swap rows 2 and 3.
So I press 2, and a comma,
and 3, and close the parentheses.
Press enter. And what I've got displayed here
is the original matrix with the second and third rows
swapped around. so instead of 7-8-9
and then 1-2-3, I've got 1-2-3
and then 7-8-9. Now if I do another operation right now,
this new matrix will be lost. If I want to save it,
I've go to store it. So to do that I press the 'store' button.
That says we're taking the answer and storing it.
We have to tell it what to store it as. I'm gonna store it as
another matrix. So in this case,
I'm going to store this as matrix 'B'. There's already something there as matrix 'B',
but this will just overwrite it.
So the calculator is saying it's go to store the answer
as matrix 'B'. I'll press 'enter' to tell it to go ahead,
and there's matrix 'B'.
So for row swap, once again, what you're going to do
is tell the calculator the name of the matrix -- that's something we always do
when we're dealing with matrices
and the numbers of the two rows that we're going to swap.
Okay, let's clear this, display the matrix again,
matrix 'A', and
go on and see about
adding a row to another row. So once again, to get to this operation I go to the matrix
menu,
go over to math, press the 'up' button.
And what I want is this item D,
row+. Now to add a row to another row, I have to tell the calculator
the name of the matrix, the row I'm going to add,
and the row I'm going to add it to. So this is matrix 'A'.
I need a comma after it.
And I wanted to add row 1 to row 2.
So I'll enter a '1', and the comma,
and '2', close the parentheses, and press 'Enter'.
And now, row 2
has become the sum of the old rows 1 and 2.
So I had a 4 and a 7... they added up to 11,
5 and 8 became 13,
and 6 and 9 became 15. Notice that the original row 1
has not changed. The only thing that changed is row 2,
the row that I added that first row onto.
So once again, the procedure for this
is to tell the calculator the name of the matrix,
the row you're adding, and the row you're adding to.
Okay. So I'll clear this again, display matrix 'A',
and
let's see about multiplying a row in a matrix.
Go the matrix menu, over to math,
press up. And we want item E,
'times row'.
The input for this is the amount of times we want to multiply
a row ---
in my example here I want to multiply 3 times row 2.
So there's a 3 here for the amount of times that I multiply the row,
then a comma,
then I've got to tell it the matrix name,
so we go to the matrix menu. We're doing this to matrix 'A',
a comma again,
and the row I'm multiplying is row 2.
I'll close the parentheses and press Enter.
And the old row 2 was 7-8-9.
For the new row 2, each of those numbers was multiplied by 3.
So 3 times 7 is 21,
3 times 8 is 24, and 3 times 9 is 27.
So to review the input for this operation...
you start out with the multiplier,
then the matrix name, and then the row that you want to multiply.
Let's go on to another one.
In this one we're going to once again multiplier a row,
and then we're going to add that to another row.
I'll clear the screen,
display matrix 1, or 'A'...
You don't have to display the matrix first. I'm just doing it so we can
compare
what we start with and the result.
I'll go to the matrix menu again,
over to math, press up, and on
the very bottom line, the item 'time-row-plus'
is what we're looking for.
So the format for this is; I have to once again tell the calculator
the multiplier, how many times I'm going to multiply the row,
then the name of the matrix,
the row I want to multiply, and then
the row I want to add that product to. So I want to
multiply 4
times... in matrix 'A',
4 times
row 3 and add that to row 2.
at yeah tour 02
So row 3 was 1-2-3.
That hasn't changed. But then we multiplied
each those elements by 4. So 4 times 1 is 4,
that got added to the 7 in row 2
and we go an 11. 4 times 2 is 8,
it's added to the 8 in row 2, and we get 16.
And 4 times 3 is 12. That gets added to the 9
in row 2, and we get 21.
So again, the format for this is
you have to tell the calculator the multiplier, the matrix name,
the row you want to multiply, and then
the row you want to add the product to.
So that's row operations in TI-83/84 calculators.
Take care, I'll see you next time.