A qustion that my solution differs from the answer of the book

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In summary, the conversation is about a question regarding finding a vector v in a given equation. The first part of the solution involves finding a vector v such that T-1=b, but this is incorrect as it is a subscript and not a superscript. The second part of the solution involves solving T-1v=b by row reducing the augmented matrix with A itself. Additionally, if asked to solve A-1v=b, it is not necessary to find A-1 and then solve the equation, but rather to multiply vector b by A.
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You are misreading the question. They are not asking you to find vector v such that T-1= b. The "-1" is a sub script, not superscript. They have defined Ta and asked you to solve T-1v= b. In other words, Ta with a= -1. Just row reduce the augmented matrix with A itself,, not A inverse.

By the way, if they were asking you to solve A-1v= b when they had given you A, you certainly should not find A-1 and then solve the equation! If you know A, the you know that AA-1v= v= Ab. Just multiply vector b by A.
 

1. Why does my solution differ from the answer in the book?

There could be several reasons for this. It's possible that the book has a mistake or typo in the answer. It's also possible that you made a mistake in your calculations or approach. Additionally, there may be more than one correct solution to the problem.

2. How do I know if my solution is correct if it differs from the book's answer?

One way to check the correctness of your solution is to double-check your calculations and make sure you followed all steps correctly. You can also ask for feedback from a peer or a teacher to see if they arrived at a similar solution. Ultimately, as long as your solution is logically sound and supported by evidence, it can be considered correct.

3. Should I always try to match the answer in the book?

While it's important to understand the solution provided in the book, it's not necessary for your solution to match it exactly. As long as you understand the concepts and can apply them correctly, it's okay for your solution to differ. In fact, having a different approach can help you understand the problem better.

4. Can my solution still be considered correct even if it differs from the book's answer?

Yes, as long as your solution is logically sound and supported by evidence, it can be considered correct. Remember, there may be more than one correct solution to a problem. It's important to understand the concepts and be able to apply them, rather than just matching the answer in the book.

5. How can I improve my problem-solving skills if my solution consistently differs from the book's answer?

If you find that your solutions often differ from the book's answer, it may be helpful to review the concepts and practice more problems. You can also try discussing your approach with a peer or a teacher to see if there are any gaps in your understanding. Remember, problem-solving skills improve with practice and perseverance.

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