The unknown vector v satisfies and where lambda, b and c are fixed and known.
Find v in terms of lambda, b and c
At first I was thinking of expanding everything out, and so I'd get:
But then that didn't seem to help. Any ideas?
The unknown vector v satisfies and where lambda, b and c are fixed and known.
Find v in terms of lambda, b and c
At first I was thinking of expanding everything out, and so I'd get:
But then that didn't seem to help. Any ideas?
Hey Educated.
Hint: You have three unknowns (v1,v2,v3) and four equations that are linear. Try setting up a linear system and reducing to get v1,v2,v3 in terms of your other known parameters. Also if there is any chance for in-consistency, then deal with that as well (there shouldn't but you need to check since you have four equations in three unknowns).
Personally, I don't like to use matrices to solve systems of equations.
you have
Multiply the first equation by to get and the second equation by to get . Those equations both have " so subtracting the second fro the first eliminates giving . Now the fourth equation has only and so we can eliminate either of those.
For example, if we multiply by we get and adding that to gives (b_1^2+ b_2^2+ b_3^2)v_2= b_2\lambda+ b_1c_3- b_2c_1[/tex] and can soplve for .