Locate mistake in matrix inverse

Question

I recently asked a question about RREF and have incorporated the helpful responses into my problem. I get the same answer every time but it is incorrect.

Does anyone know what I am doing wrong?

Thanks again.

Answer 1

You made a mistake at

$R_1 + R_3 \to R_3,$

the last row should be $\begin{bmatrix} 0 & 1 & 4 & 1 & 1 & 1 \end{bmatrix}$

Remark:

• $R_i + cR_j \to R_i$ is an elementary step.
• $R_j + cR_i \to R_i$ is actually two steps, it consists of $R_i + \frac1cR_j \to R_i$ and $cR_i$.
• That is where you store the result matters.
• While we can't see the difference now, it plays a role when you compute determinant.

Answer 2

You make a mistake here: $$R_1-R_2\to R_1$$ because in that line $R_1-R_2$ is $$1\quad -1\quad 0\quad\mid\quad 1\quad -4\quad 12.$$