How to Solve Simultaneous Linear Equations Using Matrices on the TI-82
1) Arrange the linear equations to be solved so they have the form Ax + By = C.
Example: Using the equations above, we have 3x + 2y = 5 and 5x +4y = 27.
2) Write these equations in matrix form, using the coefficients A, B, and C to fill in the matrix.
The matrix for these equations would look like this:
3 2 5
5 4 27
The first column is a list of the x coefficients, the second column is a list of the y coefficients, and the third column is a list of values.
3) Turn on the TI-82, hit the [Matrix] key, select "Edit", select the name of a matrix that you want to use to solve this problem (A-E), and hit [Enter].
Example: We'll say that you've chosen to use matrix A for the coefficient matrix.
4) Define the size of your coefficient matrix.
Example: In this case, our coefficient matrix is two rows-by-two columns, so press "2" [Enter] "2" [Enter]. A problem that requires solving three equations in three unknowns will require a 3x3 coefficient matrix.
5) Enter the coefficients into the matrix in the calculator and then Quit.
Example: Press "3" [Enter] "2" [Enter] "5" [Enter] "4" [Enter][Quit]
6) Hit the [Matrix] key, select "Edit", select the name of a second matrix that you want to use to solve this problem (A-E), and hit [Enter].
Example: We'll say that you've chosen to use matrix B for the value matrix.
7) Define the size of your value matrix.
Example: In this case, our value matrix is two rows-by-one column, so press "2" [Enter] "1" [Enter]. A problem that requires solving three equations in three unknowns will require a 3x1 coefficient matrix.
8) Enter the values into the matrix in the calculator and then Quit.
Example: Press "5" [Enter] "27" [Enter][Quit]
9) Hit the [Matrix] key again, select Matrix A, hit [Enter], hit [x^-1], hit[*], hit [Matrix], select Matrix B, hit [Enter], then hit [Enter] again.
Example: [A]^-1 * [B]
NOTE: You MUST select the matrix name from the Matrix menu -- you cannot simply type in [A]!
This command tells the calculator to invert the first matrix, then multiply it by the second matrix, to get a matrix that lists your solutions in order. It's not critical that you understand this step, although the mathematical process is pretty cool!
10) Interpret Your Answer.
What appears on the calculator screen is this:
[[-17]
28]]
The -17 is the solution for the first variable, "x", and the 28 is the solution for the second variable, "y".
Using matrices to help you find solutions to simultaneous linear equations is one of the ways that graphing calculators can assist your problem-solving in physics. Please make sure, however, that you don't become TOO dependent on the calculator. Being able to manipulate variables and equations "by hand", as well as being able to substitute and solve equations in several unknowns is a valuable skill that cannot be replaced with a calculator, however powerful it may be.
http://www.ecs.umass.edu/~chang/TI83.htm
Speedy
