My Pearson textbook is showing solutions to "find the LU factorization of the given matrix" problems with (-1)s appearing in L's main diagonal. However when multiplying the two matrices in the solution, it does not return the original given matrix (either wrong signs in the row that has a (-1) or completely incorrect entries. Am I missing something or is this textbook just as shitty as I think it is?
Here's two examples I found in the book:
I'm getting an LU for 7 as L = $\bigl(\begin{smallmatrix}1&0\\-3/2&1\end{smallmatrix}\bigr)$ U = $\bigl(\begin{smallmatrix}2&5\\0&7/2\end{smallmatrix}\bigr)$ and an LU for 11 as L = $\bigl(\begin{smallmatrix}1&0&0\\2&1&0\\-1/3&1&1\end{smallmatrix}\bigr)$ U = $\bigl(\begin{smallmatrix}3&-6&3\\0&5&-4\\0&0&5\end{smallmatrix}\bigr)$ When multiplying each respective pair, I get the original given matrix...
One method of LU starts with $L$ as the identity matrix.
Then, after row operations, you get $$L = \begin{bmatrix} 1 & 0 \\ -\dfrac{3}{2}& 1\end{bmatrix},~~ U = \begin{bmatrix} 2 &5 \\ 0 & \dfrac{7}{2} \end{bmatrix}$$
This agrees with your first result.
There is a sign error in your second result (location is $a_{23}$)
$$L = \begin{bmatrix} 1&0&0\\ 2&1&0\\-\dfrac{1}{3} & 1 & 1\end{bmatrix}. ~~ U = \begin{bmatrix} 3&-6&3\\ 0&5&-4\\0&0&5 \end{bmatrix}$$
Those are obvious typos in the book solution.
Which book is this? Did you check the errata?