hi,

since I can't find solutions to all exercises of Prof. Strang's Introduction to linear algebra 4th ed, I need to ask you folks :) i've tried to calculate all of the exercises by myself, but now I have no way of checking correctness of my answers. Can someone please post solution to 1.1 ex. 29?

My solution was:
29) two different combinations are i.e. u-v+w=b or -2u+v=b. as for the second part of the question: I believe the answer is NO, since "any three vectors" can also mean linear dependent vectors which won't always add up to (0,1).

Question

hi,

since I can't find solutions to all exercises of Prof. Strang's Introduction to linear algebra 4th ed, I need to ask you folks :) i've tried to calculate all of the exercises by myself, but now I have no way of checking correctness of my answers. Can someone please post solution to 1.1 ex. 29?

My solution was:
29) two different combinations are i.e. u-v+w=b or -2u+v=b. as for the second part of the question: I believe the answer is NO, since "any three vectors" can also mean linear dependent vectors which won't always add up to (0,1).

anonymous · Answer

I have the solutions to the textbook, so u can post your email addr,and I will email it to you~!

anonymous · Answer

For the second part, any two independent vectors in R^2 span the whole plane.  So as long as none of the three vectors is a multiple of the other, then there can be two combinations of those vectors to add up to (0,1).  Indeed, if none of the three vectors (as lines from the origin) lie on the same line as the other two, then there is exactly three combinations to add up to (0,1).  Otherwise, there can at most be one such combination.  So the answer is no.  Hope this makes sense.

anonymous · Answer

All solutions can be found at this link http://www.scribd.com/doc/164435523/Gilbert-Strang-ILA4

delahruza · Answer

jcw411 absolutely brilliant :) thank You!