how to do matrices on ti-84 plus This is a topic that many people are looking for. cfiva.org is a channel providing useful information about learning, life, digital marketing and online courses …. it will help you have an overview and solid multi-faceted knowledge . Today, cfiva.org would like to introduce to you Matrix Operations on the TI-83+ TI-84+. Following along are instructions in the video below:
Is a basic primer for using the ti 84. Plus. Or the ti 83 plus plus calculator to work with matrices.
We are going to enter matrices into the calculatorre going to do some basic operation on matrices and were going to solve a system of equations two different ways using matrices to enter a matrix you go to the second key in the upper left hand corner of the keyboard press. It once and then press the key with with the x to the negative one. It has the word matrix right above.
It this brings us to the matrix menu here youll see weve got three sub menus. The names in which we can pick the name of each matrix abcdefg and then theres a few more the math operations determinant identity. So forth lots of different operations on the matrices and then finally our third menu.
Here is edit in which we can use this menu to enter elements into a matrix or to change elements in an existing matrix so heres where we want to start. Were going to edit matrix. A by default matrices.
Are one by one in the calculator. So im going to change this to a two by two matrix by going to enter to enter and now you see weve got four elements a two by two matrix where we can start putting the elements of the matrix in so im going to put in negative two two five and negative four one thing to be careful of when you put in elements of a matrix. If one of those elements is negative use this key down here to indicate that its negative.
Not this thats the subtraction key different okay lets have a look at our matrix.
So im going to hit second matrix. Im going to hit enter to pick the name of matrix. A notice that the variables have a bracket around them to indicate its a matrix when i hit enter this lets me see the elements of the matrix just like i entered.
Im going to enter a second matrix now now suppose i want to add matrix. A and matrix b. Together.
Use the addition sign just like you would with regular numbers. And we see theyre added together if we want to multiply matrices together we can just use the multiplication symbol here. Im going to use the shortcut of 2nd last entry and then im going to backspace here to just change this one symbol and like so multiplication.
I can also multiply by real numbers for instance five multiplied by matrix a and we see that every element in matrix. A has been multiplied by five now the real lifting power of the calculator is to do things like finding the determinant and finding the inverse of a matrix we can find the determinant like this second matrix and then we go to math. And its the first one on the list det and this will find the determinant of matrix a negative 2.
If we want to find the inverse of matrix a we use our x to the power negative. 1 key look at that very speedy and quick now we know that this is the the inverse because when we multiply a matrix by its inverse. It gives us the identity matrix.
Watch this a multiplied by its inverse heres the identity matrix.
A 2×2 now. Suppose we want to solve this system of equations. 2x.
Plus. 3y. Minus z.
Is equal to 11. 3x. Minus.
2y. Plus. 4z is equal to 10 and x.
Plus. 4y. Minus.
2z is equal to 8.
We want to put in the coefficients of all the variables in a 3×3 matrix. Im going to edit matrix a to be a 3×3 and im going to enter the coefficients of the equation. 2 3.
Negative. 1 3. Negative.
2 4. 1. 4.
And negative. 2. Now the second matrix is going to be a three by one and those are going to be 11 10 and 8.
So how do we use these two matrices to solve the system. We take the inverse of matrix a and multiply it by that 3 by 1 matrix. Which we put in b.
And the resulting matrix are the answers to our equations x.
Is 4. Y. Is 1.
And z is 0. The second way to solve this system of equations is to use an augmented matrix. Now what im going to do is im going to use the augment command to attach that 3.
By 1 matrix b to matrix a and im going to store it in c. Now. We see here that matrix p.
Has been augmented to matrix a so now we have a matrix that is four columns and 3 rows. If we use the rref command. Which is under math be rref reduced row echelon form and we apply it to this augmented matrix.
Which remember it was called c. Here we get what looks kind of like a three by three identity matrix. But here again are the answers.
4. Would be 4 x. 1.
Would be 4 y and 0. Would be 4 see .
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