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

[transgalactic]

the question is:
http://img170.imageshack.us/my.php?image=40507375yw6.jpg

the first part of the solution:
http://img206.imageshack.us/my.php?image=g001pe5.jpg

the second part of the solution:
http://img206.imageshack.us/my.php?image=g002uk6.jpg

 

[HallsofIvy]

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 T_a and asked you to solve T_-1v= b. In other words, T_a 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.