SOLUTION: what are the steps when using a graphing calculator to solve systems using inverse matrices

Question 117507: what are the steps when using a graphing calculator to solve systems using inverse matrices
Answer by bucky(2189) (Show Source): You can put this solution on YOUR website!
Probably varies depending on the model of the calculator. On the TI-89 it goes this way:
.
Suppose you are given a 3 by 3 matrix to inverse. And suppose that matrix is:
.
+1 0 0
-1 1 0
+1 1 1
.
The plus signs are just added for typing purposes in this answer. The minus sign is needed,
but the plus signs are just inserted to keep the columns of numbers aligned in the typed
version.
.
On the entry line ... enter exactly as below:
.
([1,0,0;-1,1,0;1,1,1])^-1
.
A couple of notes about this entry:
.
Note that there is a difference between the symbols "(" and "[" and their counterparts in
the reverse direction. Do not interchange them or use a parenthesis in place of a bracket.
.
Note that the symbol representing the end of a line in the matrix is a semicolon, not
a colon.
.
Note that the minus sign at the beginning of the second line is from the key that looks
like (-). It is not the subtraction function key that has just a minus sign on it. The same
thing applies for the minus sign in the exponent ... use the (-) key not the - key to
enter the exponent -1.
.
When you type the line exactly as shown above, you are raising the matrix to the minus 1 power.
.
You will get an answer that shows the inversed matrix is:
.
+1 +0 0
+1 +1 0
-2 -1 1
.
As before, the plus signs are added here just to keep the number columns aligned. They
do not show in the calculator's answer but the columns are aligned.
.
Hope this helps you with your calculator. If it does not, read your instruction book on how
to enter a matrix. Then try raising it to the -1 power to see if that procedure works.
Use the problem and the answer above as a check to see if the calculator gives the answer
above.
.
Hope this helps you out ...

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