# Help on systems of eqtns.

1. Jan 25, 2008

Need some help to solve this problem.I have tried using a system of equation(matrices) but hasnt worked out.

Find nonzero scalars a,b and c such that aA+b(A-B)+c(A+B)=0 for every pair of vectors A and B.

Thanks for the help.

2. Jan 25, 2008

### Staff: Mentor

What do you mean by "vectors"? If A and B are vectors, and they are orthogonal to each other, I don't believe there is a general solution.

EDIT -- oops, yeah there still is a set of solutions. Just distribute the terms, and gather the terms multiplying A and those multiplying B. Assume that A and B are indeed orthogonal. What can you say about those two sets of terms....?

3. Jan 25, 2008

### HallsofIvy

Staff Emeritus
For every pair of vectors A and B? Do you mean one set of numbers a, b, c such that that is true for all vectors? Obviously that is impossible.

If it were true for all A, B, it must be true for any A and B= 0. Then you must have (a+ b+ c)A= 0 for any A, that is a+ b+ c= 0.

On the other hand, if A= B, you have (a+ 2c)A= 0 so a+ 2c= 0. If A= -B, you have (a+ 2b)A= 0 so a+ 2b= 0. The only numbers that satisfy those three equations are a= b= c= 0.

If, however, you mean find a, b, c so that aA+ b(A- B)+ c(A+ B)= 0 for specific A, B, then you need to have (a+ b+ c)A+ (a- b+ c)B. There will be an infinite number of values of a, b, c such that that is true for any given A and B.

4. Jan 25, 2008

Hmm, the book says one possible answer is a=-2,b=c=1

5. Jan 25, 2008

### Rainbow Child

What is the exact statement of the problem from your book? Does it says anything about the vectors A,B, independent or something else?

6. Jan 25, 2008

what i posted is the EXACT statement, its from a vector analysis course.

7. Jan 25, 2008

### Rainbow Child

Ok, then! If A,B are arbitrary vectors I would write

<< exact solution edited out by berkeman, but too late to keep the OP from seeing it >>

yielding the book's solution, but I assumed that A,B are arbitrary vectors.

Last edited by a moderator: Jan 28, 2008
8. Jan 25, 2008

### jostpuur

I hope nobody succeeded seeing my previous post, which I deleted quickly. I cannot believe how frozen my brains were.....

9. Jan 25, 2008

Ahh!cant believe this easy question gave me problems..so that answer is one of many possible answers just like the book says!..thnx for the help!

10. Jan 28, 2008

### Staff: Mentor

Only the Mentors can see it. We're wispering about it now....