How to solve this problem? Help Me.?

Question

Consider a base A, B, C and a vector
-2A+3B-C
Compute the co-ordinates of this vector relatively to the base P,Q,R
where
P=2A-3B, Q=A-2B+C,R= -3A+B+2C.

Well..this is from vector algebra.Help me..

Answer 1

so we have
P = 2 A - 3 B
Q = A-2B+C
R = -3A+B+2C.

And we want to solve
1) a*P + b*Q + c*R = -2 A
2) a*P + b*Q + c*R = 3 B
3) a*P + b*Q + c*R = - C

That's 3 equations and 3 unknowns (a,b,c). Remember P,Q, & R can be put in terms of A,B,C. Just work those guys out and figure out what a, b, c must be in order for those eq's to work out.

I have little doubt that the Euler dude answered this correctly for you, but I just figured that you might need to see what was going on there so you can do it yourself.

Answer 2

First you want to solve for A, B, and C in terms of P,Q,R.

To do this, you need to solve the system of equations
2A-3B=P
A-2B+C=Q
-3A+B+2C=R

I'll work on these and finish this problem in a sec.

Ok, I have
A=(-5P+6Q-3R)/5=<-1, 6/5, -3/5>
B=(-5P+4Q-2R)/5=<-1, 4/5, -2/5>
C=(-5P+7Q-R)/5=<-1, 7/5, -1/5>

Thus -2A+3B-C=-(2A-3B)-C= -(P)-(-5P+7Q-R)/5= -(7Q+R)/5=<0,-7/5, 1/5>

Answer 3

<-3B, A-B+C, -3A+B+C>

Answer 4

CAN U HELP ME HOE DO I POST ?