I can't phrase my problem well, so I have to give an example here.
I was doing this algebra problem
1 Write down the 3 by 3 matrices that produce these elimination steps:
(a) E21 subtracts 5 times row 1 from row 2.
(b) E32 subtracts -7 times row 2 from row 3.
(c) P exchanges rows 1 and 2, then rows 2 and 3.
The answer to question (a) is straightforward
| 1 0 0 |
| -5 1 0 |
| 0 0 1 |
Now please pay attention to question (b)
The correct answer should be
| 1 0 0 |
| 0 1 0 |
| 0 7 1 |
In principle if I could do question (a), question (b) is just the same concept.
But I gave the wrong answer, my answer was
| 1 0 0 |
| 0 1 0 |
| 0 -7 1 |
I made this mistake is because I didn't notice the minus sign before 7.
I saw it ,but it didn't register during problem solving procedure.
Had the question be phrased, add 7 times row 2 to row 3, I would've given the correct answer.
I understand the concept and procedure to answer the question, but made a mistake.
I often make this kind of mistakes, my parents always yell at me when I do that, but I continue make this kind of mistakes.
Could someone please explain to me, why am I make such errors? do other people also make mistakes like I do? What can I do so I stop or make fewer mistakes of this kind?