Difference between ref and rref on TI-89?

Question

What is the difference between ref and rref on the TI-89?

Can someone do a simple matrix problem by hand. I'm a little rusty on the subject.. such as for

2x - 4y = 2

x + 3y = 7

or come up with your own.

Answer 1

ref returns the reduced echelon form

rref returns the row reduced echelon form.

I believe you would want to use rref to get that answer.

Try this on the TI-89 for the example you gave.  What does the following on your calculator give you?

rref(2 -4 2; 1 3 7)

Does it give the correct answer?  It should return

(1 0 3.4; 0 1 1.2)

Anyway...

Ax=b

A is a matrix (2x2), x is a vector (2x1), b is a vector (2x1).

A = [2 -4; 1 3] {A11 = 2, A12 = -4, A21 = 1, A22 = 3}

x = [x; y]  {x11 = x, x21 = y}

b = [2; 7]  {b11 = 2, b21 = 7}

Since

Ax=b

Then

(A^-1)A*x=(A^-1)*b

Since

(A^-1)A = I {I = Identity Matrix}

x = (A^-1)*b

Using Octave...

A^-1 = [1/3 2/5; -1/10 1/5]

The answer is then

x  = [3.4; 1.2]

It means that x=3.4 and y=1.2

Those values are indeed correct upon trial in both equations.