Linear algebra againn please help!

H

hayood

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Feb 16, 2010
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Let u=(-3,2,1) v=(4,0,-8), and w= (6,-1,-4 ) which are vectors. Find scalars c1,c2 , and c3 such that :
c1u+c2v+c3w = (2,0,4)
 
Isn't it just:

-3C1 + 4C2 + 6C3 = 2
+2C1 + 0C2 -1C3 = 0
+1C1 - 8C2 - 4C3 = 4

solve
 
C1, C2 and C3 are your unknowns in this new system of linear equations. This is how you solve for them. Plug those 3 equations into a matrix and solve.
 
yup, that would be the easy way to do it. And that'll give you the values of c1, c2 and c3

Or you can try substitution (I wouldn't) or elimination (a good method for this easy system)

It depends on what you're most comfortable with.
 
i did it :):) but i have a question when do you know if u have to use reduced row echelon or just row echelon.. ?
 
If you're solving a system of linear equations, you'll use reduced row echelon form (rref). The form has a 1 in each column and zeroes everywhere else in the column. ref has a leading 1 in each row, but not necessarily all zeroes thereafter. rref is more popular especially if you're just solving equations such as in this problem.
 
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