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based on simultaneous and matrixs

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2 Answers

Sorry to say this but I do not know a matrix mathematical method called Ti-84 calculator. Maybe the calculator does the solution based in any of the two methods that I know and will describe below. Matlab  has another method of solving them but based in one of the two methods described below.
I will use any of the two known methods to solve this system by hand, one is the Gauss-Jordan elimination and the other is the Cramer rule.
In the first one you create the augmented matrix and then make the changes that you need to obtain the so called canonical form. the operations will be done in the rows until the matrix with three columns as diagonal ones is obtained.
The second system ( Cramer) is obtained by calculating the Determinant of the system and then replacing the x values of the system in the first row and doing [A1]/[A]. and so on. in this system is easier to obtain directly the answers obtained by the tutor that used the T1-84 calculator that I do not have and maybe some of the students don't.
If Kennedy wants I will develop the two manual systems in this answer.
Using a TI-84 calculator, hit 2nd x^-1 or the "matrix" function.
Arrow right 2 spots to the "edit" tab and hit enter.
Type in 3 x 4.   3 enter.  4 enter.
Your matrix to solve is a 3 x 4 matrix as the problem above indicates.
(Rows by Columns, thus 3 rows and 4 columns is a 3 x 4 matrix).
 
Now enter the leading coefficient of each row into the calculator until all 12 values are entered into your calculator matrix.
i.e. - row 1 = 2 enter, 3 enter, -1 enter, 6 enter.
        row 2 = 3 enter, 1 enter, 5 enter, 8 enter.
        row 3 = 1 enter, 2 enter, 1 enter, 10 enter.
Now, hit 2nd mode(quit) button on calculator.
Then, hit matrix button again.
Arrow over 1 to the right to "math".  Alist will appear.  Arrow down until you see "rref" - which is letter B on my calculator.
Hit enter.
Hit 2nd Matrix key again. Hit enter (on matrix A).
Close the parentheses on calculator by hitting right parentheses ")".
Hit enter.
This shows your solution to your matrix.
The 3 values in the far right column are your values to x, y, and z.
The answer should probably be stated in fraction form, not decimal forms that have appeared.
To covert to fractions, hit "MATH" button on calculator, hit enter, hit enter again, and now your matrix has been converted to fractions.
The answers I get are:
 
x = -66/17.
y = 94/17.
z = 48/17.
 
(Answers in decimal form are:)
x = -3.882352941.
y = 5.529411765.
z = 2.823529412.
 
You can check your answers by substituting these answers into any or all of the 3 equations given in your problem and making sure that the result is a true statement.