since v1 =(6,7,1) v2 = (2,0,3) and v3 = (4,6,1) form a basis in R3. do I find the coordinates of (6,2,6) relative to this basis by solving this system for a ,b,c:

(6,2,6)= av1 + bv2 + cv3 and are a,b,c the coordiantes?

Question

since v1 =(6,7,1) v2 = (2,0,3) and v3 = (4,6,1) form a basis in R3. do I find the coordinates of (6,2,6) relative to this basis by solving this system for a ,b,c:

(6,2,6)= av1 + bv2 + cv3 and are a,b,c the coordiantes?

anonymous · Answer

That looks right.  You can rewrite the right hand side of the equation as a matrix times a vector (or maybe a vector times a matrix?) and then use the inverse matrix to solve.