Solve the system of linear equations by using the reef command on a graphing calculator. State your answer rounded to two decimal places

Question

Solve the system of linear equations by using the reef command on a graphing calculator. State your answer rounded to two decimal places.

	42x	−	31y	−	42w	=	−8.8
−6x	−	9w	=	4.2
35x	−	67z	+	32w	=	388.7
31y	+	48z	−	52w	=	−110.6
(x, y, z, w) =

 

 

Answer 1

I'll assume you mean RREF in the TI-84 as opposed to "reef". RREF stands for Row Reduce Echelon Form which will convert your starting augmented matrix into the row reduced form so that you can pick out the solutions to the system of equations.

This system of equations can be written in matrix form by using the coefficients. First let's write the equations making sure to put in placeholders for missing variables in the form:

Ax + By + Cz + Dw = E

1) 42x + -31y + 0z + -42w = -8.8

2) -6x + 0y + 0z + -9w = 4.2

3) 35x + 0y + -67z + 32w = 388.7

4) 0x + 31y + 48z + -52w = -110.6

Then the corresponding matrix (which BTW is called an augmented matrix) is:

Now, enter this into your calculator - I'll put it into matrix A:

1) Push the blue "2nd" button then "matrix" (two buttons below the green button) then scroll to the right to "EDIT" then select 1: [ A ]. Enter the matrix as a 4 x 5 matrix then input all the numbers as I have shown above in the augmented matrix. Double check to make sure you entered the data correctly.

Then hit the blue "2nd" and then "quit".

Then hit the blue "2nd" and then "matrix" and scroll right to math and scroll down to "rref(" (in my calculator this is selection "B:") and hit "enter". Now hit "2nd" "matrix" again and select "1: [ A ]" and hit "enter" and then close parentheses. and "enter". You'll get the Row Reduced Echelon form of the matrix where the top right number is the value of x (I got x = 1.1) and the number below that is "y", then "z" then "w"