Are These Row Equivalent Matrices? Why Am I Getting Different Results?

[Pull and Twist]

I am having trouble with the following problem;

a.) Find a matrix B in reduced echelon form such that B is row equivalent to the given matrix A.

A=$$\left[\begin{array}{c}1 & 2 & 3 & -1 \\ 3 & 5 & 8 & -2 \\ 1 & 1 & 2 & 0 \end{array}\right]$$

So using my calculator I am able to get,

B=$$\left[\begin{array}{c}1 & 5/8 & 8/3 & -2/3 \\ 0 & 1 & 1 & -1 \\ 0 & 0 & 0 & 0 \end{array}\right]$$

The problem is that the book claims that B should be;

B=$$\left[\begin{array}{c}1 & 2 & 3 & -1 \\ 0 & -1 & -1 & 1 \\ 0 & 0 & 0 & 0 \end{array}\right]$$

Which is weird cause according to the row equivalency theorem, any B of A in REF should be the same unique row equivalent matrix. Why am I not getting the same result?? I am using a TI-83 Plus.

 

[Deveno]

I am having trouble with the following problem;

a.) Find a matrix B in reduced echelon form such that B is row equivalent to the given matrix A.

A=$$\left[\begin{array}{c}1 & 2 & 3 & -1 \\ 3 & 5 & 8 & -2 \\ 1 & 1 & 2 & 0 \end{array}\right]$$

So using my calculator I am able to get,

Unfortunately, we cannot verify your calculator input, nor the accuracy of said calculator. Sorry about that.

B=$$\left[\begin{array}{c}1 & 5/8 & 8/3 & -2/3 \\ 0 & 1 & 1 & -1 \\ 0 & 0 & 0 & 0 \end{array}\right]$$

The problem is that the book claims that B should be;

B=$$\left[\begin{array}{c}1 & 2 & 3 & -1 \\ 0 & -1 & -1 & 1 \\ 0 & 0 & 0 & 0 \end{array}\right]$$

Which is weird cause according to the row equivalency theorem, any B of A in REF should be the same unique row equivalent matrix. Why am I not getting the same result?? I am using a TI-83 Plus.

only RREF is unique, the matrix in your book appears to be properly calculated, but it is NOT in RREF, nor is your matrix $B$ (you have non-zero entries in row 1 above the leading one in row 2, as does the matrix in your book). The RREF can be found here:

Wolfram|Alpha: Computational Knowledge Engine

I verified your book's answer, using the following steps:

a) Subtract 3 times row 1 from row 2
b) Multiply row 2 by -1
c) Subtract row 1 from row 3
d) Add row 2 to row 3

Row-reduction is a path fraught with peril, simple mistakes can ruin everything.